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Numerical Algorithms by E. V. Krishnamurthy
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1Microsoft Research Audio 103751: Numerical Algorithms In Material Science
By Microsoft Research
The talk will consist of two parts. In the first part, I will present prior work aimed at developing new algorithms for materials science applications. I developed a novel numerical method to optimize the shape of mechanical parts and maximize their strength. This optimization problem was extremely challenging as it involved changing the topology and therefore classical optimization methods do not apply. A similar idea can be applied to model shape memory alloys and plasticity in metals. In this project, the optimization led to the construction of a tree of laminated microstructures. Constraints from mechanical equilibrium were used to construct an adaptive tree and to determine the optimal number of levels. The second part involves more recent work. I will present the implementation of a new heat flux algorithm to understand failures in micro-devices in LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator); LAMMPS is a high performance code which was benchmarked on Blue Gene L with 90% parallel efficiency. Also I am currently extending the capabilities of ParaDiS (Parallel Dislocation Simulator), another high performance code which has run on 135k processors of Blue Gene L. ©2008 Microsoft Corporation. All rights reserved.
“Microsoft Research Audio 103751: Numerical Algorithms In Material Science” Metadata:
- Title: ➤ Microsoft Research Audio 103751: Numerical Algorithms In Material Science
- Author: Microsoft Research
- Language: English
“Microsoft Research Audio 103751: Numerical Algorithms In Material Science” Subjects and Themes:
- Subjects: ➤ Microsoft Research - Microsoft Research Audio MP3 Archive - Laurent Visconti - Sylvie Aubry
Edition Identifiers:
- Internet Archive ID: ➤ Microsoft_Research_Audio_103751
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2DTIC ADA288754: A Multiresolution Representation And Numerical Algorithms: A Brief Review.
By Defense Technical Information Center
In this paper we review recent developments in techniques to represent data in terms of its local scale components. These techniques enable us to obtain data compression by eliminating scale-coefficients which are sufficiently small. This capability for data compression can be used to reduce the cost of many numerical solution algorithms by either applying it to the numerical solution operator in order to get an approximate sparse representation, or by applying it to the numerical solution itself in order to reduce the number of quantities that need to be computed.
“DTIC ADA288754: A Multiresolution Representation And Numerical Algorithms: A Brief Review.” Metadata:
- Title: ➤ DTIC ADA288754: A Multiresolution Representation And Numerical Algorithms: A Brief Review.
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA288754: A Multiresolution Representation And Numerical Algorithms: A Brief Review.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Harten, Ami - INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA - *ALGORITHMS - *NUMERICAL ANALYSIS - *DATA COMPRESSION - COMPUTATIONS - DATA MANAGEMENT - MATRICES(MATHEMATICS) - RESOLUTION - TRANSFORMATIONS(MATHEMATICS) - SOLUTIONS(GENERAL) - APPROXIMATION(MATHEMATICS) - INTERPOLATION - OPERATORS(MATHEMATICS) - INTEGRAL EQUATIONS - FOURIER ANALYSIS.
Edition Identifiers:
- Internet Archive ID: DTIC_ADA288754
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3DTIC ADA318799: Numerical And Symbolic Algorithms For Application Specific Signal Processing.
By Defense Technical Information Center
In this paper we review recent developments in techniques to represent data in terms of its local scale components. These techniques enable us to obtain data compression by eliminating scale-coefficients which are sufficiently small. This capability for data compression can be used to reduce the cost of many numerical solution algorithms by either applying it to the numerical solution operator in order to get an approximate sparse representation, or by applying it to the numerical solution itself in order to reduce the number of quantities that need to be computed.
“DTIC ADA318799: Numerical And Symbolic Algorithms For Application Specific Signal Processing.” Metadata:
- Title: ➤ DTIC ADA318799: Numerical And Symbolic Algorithms For Application Specific Signal Processing.
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA318799: Numerical And Symbolic Algorithms For Application Specific Signal Processing.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Oppenheim, Alan V. - MASSACHUSETTS INST OF TECH CAMBRIDGE RESEARCH LAB OF ELECTRONICS - *SIGNAL PROCESSING - *DIGITAL FILTERS - THROUGHPUT - INPUT OUTPUT DEVICES - FAULT TOLERANT COMPUTING - DELAY LINES.
Edition Identifiers:
- Internet Archive ID: DTIC_ADA318799
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4DTIC ADA327659: Numerical Algorithms In A Lagrangian Hydrocode.
By Defense Technical Information Center
This report documents the numerical algorithms used in an explicit Lagrangian finite element hydrocode. One, two, and three dimensional implementations of the numerical solution of the conservation equations are covered. Triangular and tetrahedral continuum elements and shell elements are described. SPH (Smooth Particle Hydrodynamics) techniques are discussed. Slideline techniques are explained. Material models are presented for constitutive behavior and equation of state behavior for several categories of materials. This report is a comprehensive presentation of the numerical techniques used in a current production hydrocode.
“DTIC ADA327659: Numerical Algorithms In A Lagrangian Hydrocode.” Metadata:
- Title: ➤ DTIC ADA327659: Numerical Algorithms In A Lagrangian Hydrocode.
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA327659: Numerical Algorithms In A Lagrangian Hydrocode.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Johnson, G. R. - ALLIANT TECHSYSTEMS INC HOPKINS MN - *ALGORITHMS - *STRUCTURAL MECHANICS - *HYDRODYNAMIC CODES - STRESS STRAIN RELATIONS - MATHEMATICAL MODELS - EQUATIONS OF MOTION - FINITE ELEMENT ANALYSIS - SHELLS(STRUCTURAL FORMS) - CONTINUUM MECHANICS - FRACTURE(MECHANICS) - STRUCTURAL RESPONSE - AXISYMMETRIC - NUMERICAL METHODS AND PROCEDURES - EQUATIONS OF STATE - LAGRANGIAN FUNCTIONS.
Edition Identifiers:
- Internet Archive ID: DTIC_ADA327659
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5DTIC ADA324028: Aircraft Icing Algorithms Applied To U. S. Navy Numerical Model Data: A Verification Study.
By Defense Technical Information Center
The results from a verification with pilot reports of four aircraft icing algorithms applied to Navy global numerical model data are presented. Significant differences in forecast performance among algorithms are closely related to differences in temperature and moisture thresholds utilized to infer icing. Near 850 mb (-5000 ft), three of the icing routines correctly forecast over 70% of observed icing occurrences, and obtained Hanssen and Kuipers skill scores (difference between hits and false alarms) in excess of 0.5 (0, random performance; I, perfect skill). Statistical tests indicated that differences in skill scores as a function of forecast lead time (0 to 24 hr) were generally not significant. The use of higher vertical resolution data was found very important for enhanced icing prediction performance. Overall results indicate that the ability of icing routines to differentiate icing type and intensity based on temperature, moisture and stability criteria is clearly limited. In terms of forecast skill and computational efficiency, algorithm comparisons indicate that the icing routine currently used as operational guidance at the National Centers for Environmental Prediction Aviation Weather Center would be a good selection for the Naval Research Laboratory's aviation support product suite.
“DTIC ADA324028: Aircraft Icing Algorithms Applied To U. S. Navy Numerical Model Data: A Verification Study.” Metadata:
- Title: ➤ DTIC ADA324028: Aircraft Icing Algorithms Applied To U. S. Navy Numerical Model Data: A Verification Study.
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA324028: Aircraft Icing Algorithms Applied To U. S. Navy Numerical Model Data: A Verification Study.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Vogel, G. N. - NAVAL RESEARCH LAB MONTEREY CA DECISION AID SECTION - *MATHEMATICAL MODELS - *ALGORITHMS - *STATISTICAL TESTS - *NAVAL RESEARCH - *AVIATION SAFETY - *ICE FORECASTING - TEMPERATURE - STABILITY - COMPUTATIONS - AIRCRAFT - SKILLS - VERIFICATION - PREDICTIONS - PILOTS - RESOLUTION - INTENSITY - EFFICIENCY - FALSE ALARMS - ICE FORMATION - AERONAUTICS - GUIDANCE - MOISTURE - SCORING - LEAD TIME - ICE REPORTING.
Edition Identifiers:
- Internet Archive ID: DTIC_ADA324028
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6Numerical Algorithms For Dual Bases Of Positive-Dimensional Ideals
By Robert Krone
An ideal of a local polynomial ring can be described by calculating a standard basis with respect to a local monomial ordering. However standard basis algorithms are not numerically stable. Instead we can describe the ideal numerically by finding the space of dual functionals that annihilate it, reducing the problem to one of linear algebra. There are several known algorithms for finding the truncated dual up to any specified degree, which is useful for describing zero-dimensional ideals. We present a stopping criterion for positive-dimensional cases based on homogenization that guarantees all generators of the initial monomial ideal are found. This has applications for calculating Hilbert functions.
“Numerical Algorithms For Dual Bases Of Positive-Dimensional Ideals” Metadata:
- Title: ➤ Numerical Algorithms For Dual Bases Of Positive-Dimensional Ideals
- Author: Robert Krone
- Language: English
Edition Identifiers:
- Internet Archive ID: arxiv-1201.2242
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7Parallel Numerical Algorithms
By Freeman, T. L. (T. Len), 1950-
An ideal of a local polynomial ring can be described by calculating a standard basis with respect to a local monomial ordering. However standard basis algorithms are not numerically stable. Instead we can describe the ideal numerically by finding the space of dual functionals that annihilate it, reducing the problem to one of linear algebra. There are several known algorithms for finding the truncated dual up to any specified degree, which is useful for describing zero-dimensional ideals. We present a stopping criterion for positive-dimensional cases based on homogenization that guarantees all generators of the initial monomial ideal are found. This has applications for calculating Hilbert functions.
“Parallel Numerical Algorithms” Metadata:
- Title: Parallel Numerical Algorithms
- Author: Freeman, T. L. (T. Len), 1950-
- Language: English
Edition Identifiers:
- Internet Archive ID: parallelnumerica0000free
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84. Maths IJMCAR Two Parallel Numerical Algorithms For Solving OSAMA EL GIAR
In this paper we introduce the design and implementation of two parallel algorithms for solving the general tridiagonal linear system of equations using two new parallel algorithms: Parallel splitting Gauss – Jordan and the general parallel splitting Gauss Jordan algorithms. These algorithms are very easily distributed over different number of processors. In addition our implementations are very efficient, generally a linear speed-up is obtained by increasing the number of processors
“4. Maths IJMCAR Two Parallel Numerical Algorithms For Solving OSAMA EL GIAR” Metadata:
- Title: ➤ 4. Maths IJMCAR Two Parallel Numerical Algorithms For Solving OSAMA EL GIAR
- Language: English
“4. Maths IJMCAR Two Parallel Numerical Algorithms For Solving OSAMA EL GIAR” Subjects and Themes:
- Subjects: ➤ Parallel Algorithms - Numerical Analysis - Tridiagonal Linear System of Equations - Gauss Jordan Algorithm
Edition Identifiers:
- Internet Archive ID: ➤ 4.MathsIJMCARTwoParallelNumericalAlgorithmsForSolvingOSAMAELGIAR
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9Complexity Of Sequential And Parallel Numerical Algorithms [proceedings]
By Symposium on Complexity of Sequential and Parallel Numerical Algorithms (1973 : Carnegie-Mellon University)
In this paper we introduce the design and implementation of two parallel algorithms for solving the general tridiagonal linear system of equations using two new parallel algorithms: Parallel splitting Gauss – Jordan and the general parallel splitting Gauss Jordan algorithms. These algorithms are very easily distributed over different number of processors. In addition our implementations are very efficient, generally a linear speed-up is obtained by increasing the number of processors
“Complexity Of Sequential And Parallel Numerical Algorithms [proceedings]” Metadata:
- Title: ➤ Complexity Of Sequential And Parallel Numerical Algorithms [proceedings]
- Author: ➤ Symposium on Complexity of Sequential and Parallel Numerical Algorithms (1973 : Carnegie-Mellon University)
- Language: English
“Complexity Of Sequential And Parallel Numerical Algorithms [proceedings]” Subjects and Themes:
- Subjects: Computer programming - Mathematics -- Data processing - Computer algorithms - Parallel processing (Electronic computers) - Sequential processing (Computer science)
Edition Identifiers:
- Internet Archive ID: complexityofsequ0000symp
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10NASA Technical Reports Server (NTRS) 19840012141: Mathematical Algorithms To Maximize Performance In Numerical Weather Prediction
By NASA Technical Reports Server (NTRS)
Numerical weather prediction models, which involve the solution of non-linear partial differential equations at points on an extensive three dimensional grid, are ideally suited for processing on vector machines. It was logical therefore that the new global forecast model to be implemented at the Meteorological Office should be written in vector code for the CYBER 205. In order to achieve full efficiency and to reduce storage requirements the model used 32-bit arithmetic which was found to provide high enough precision. Unfortunately, however, the trigonometrical and logarithmic functions provided by CDC could only handle 64-bit vectors and, although written in efficient scalar code, did not take advantage of the special facilities of a vector processor. It was therefore necessary to rewrite the functions in vector code to handle both 32 and 64-bit vectors. There was also no half-precision compiler available for the Cyber 205 at that time and so the functions, like the model, had to make extensive use of the special call syntax. This made the code more difficult to write but it allowed much greater flexibility in that it became possible to access the exponent of a floating-point number independently of its coefficient. A description is given of the technique and the results which were achieved are summarized.
“NASA Technical Reports Server (NTRS) 19840012141: Mathematical Algorithms To Maximize Performance In Numerical Weather Prediction” Metadata:
- Title: ➤ NASA Technical Reports Server (NTRS) 19840012141: Mathematical Algorithms To Maximize Performance In Numerical Weather Prediction
- Author: ➤ NASA Technical Reports Server (NTRS)
- Language: English
“NASA Technical Reports Server (NTRS) 19840012141: Mathematical Algorithms To Maximize Performance In Numerical Weather Prediction” Subjects and Themes:
- Subjects: ➤ NASA Technical Reports Server (NTRS) - ALGORITHMS - NUMERICAL WEATHER FORECASTING - PARTIAL DIFFERENTIAL EQUATIONS - COMPUTER PROGRAMS - DIGITAL COMPUTERS - MATHEMATICAL MODELS - PREDICTIONS - PROBLEM SOLVING - Foreman, A.
Edition Identifiers:
- Internet Archive ID: NASA_NTRS_Archive_19840012141
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11Remarks On Efficient Numerical Algorithms For Ultracomputers
By Peskin, Charles S and Widlund, Olof B
8 p. 28 cm
“Remarks On Efficient Numerical Algorithms For Ultracomputers” Metadata:
- Title: ➤ Remarks On Efficient Numerical Algorithms For Ultracomputers
- Authors: Peskin, Charles SWidlund, Olof B
- Language: English
Edition Identifiers:
- Internet Archive ID: remarksonefficie00pesk
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12Numerical Analysis Algorithms And Computation
By Murphy, J
8 p. 28 cm
“Numerical Analysis Algorithms And Computation” Metadata:
- Title: ➤ Numerical Analysis Algorithms And Computation
- Author: Murphy, J
- Language: English
Edition Identifiers:
- Internet Archive ID: numericalanalysi0000murp
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13NAG DMC User Guide - Numerical Algorithms Group
8 p. 28 cm
“NAG DMC User Guide - Numerical Algorithms Group” Metadata:
- Title: ➤ NAG DMC User Guide - Numerical Algorithms Group
“NAG DMC User Guide - Numerical Algorithms Group” Subjects and Themes:
- Subjects: manualzilla - manuals
Edition Identifiers:
- Internet Archive ID: manualzilla-id-6893342
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14Numerical Algorithms For Solving An Elliptic Optimal Control Problem With A Power-law Nonlinearity
By Hart L., Yatsechko N.
Abstract : The paper is devoted to the development and analysis of approximation-iteration algorithms based on the method of grids and the method of lines for solving an elliptic optimal control problem with a power-law nonlinearity. For the numerical solution of the main boundary value problem and the adjoint one, the second order of accuracy difference schemes are applied using the implicit method of simple iteration. Computational schemes of the method of lines for solving the above-mentioned elliptic boundary value problems are implemented in combination with the shooting method for the approximate solution of boundary value problems for the corresponding ordinary differential equations systems arising in the considered domain after lattice approximation. To minimize the objective functional, well-known gradient-type methods (gradient projection and conditional gradient methods) of constrained optimization are used. The essence of the proposed approximation-iteration approach consists in replacing the original extremal problem with a sequence of grid problems that approximate it on a set of refining grids, and applying an iterative gradient-type method to each of the "approximate" extremal problems. In this case, we propose to construct only a few approximations to the solution for each of the "approximate" problems and to take the last of these approximations, using piecewise linear interpolation, as the initial approximation in the iterative process for the next "approximate" problem. The sequence of the corresponding piecewise linear interpolants is considered as a sequence of approximations to the solution of the original extremal problem. The paper discusses the theoretical foundations of this combined approach, as well as its advantages over traditional methods using the example of solving a model optimal control problem.
“Numerical Algorithms For Solving An Elliptic Optimal Control Problem With A Power-law Nonlinearity” Metadata:
- Title: ➤ Numerical Algorithms For Solving An Elliptic Optimal Control Problem With A Power-law Nonlinearity
- Author: Hart L., Yatsechko N.
- Language: ukr
“Numerical Algorithms For Solving An Elliptic Optimal Control Problem With A Power-law Nonlinearity” Subjects and Themes:
- Subjects: ➤ optimal control problem - elliptic system - power-law nonlinearity - grid method - method of lines - approximation schemes.
Edition Identifiers:
- Internet Archive ID: 2-21_20230911_202309
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15DTIC ADA322928: Numerical Algorithms For Compressible Turbulence.
By Defense Technical Information Center
This research involves higher order methods for solving partial differential equations. A common theme of this research is the use of spectral methods. One of the challenges of the spectral Fourier method is approximating smooth functions that are non-periodic. The rate of convergence deteriorates to O(1/N) away from the boundaries and there are spurious oscillations at the boundary points, known as the Gibbs phenomenon. We discuss an analytic but non-periodic function f(x) defined on -1,1, for which the first 2N+1 Fourier coefficients are known, and focuses on two methods that successfully eliminate the Gibbs phenomenon based on the information obtained from the Fourier coefficients. A new method is suggested to improve upon the results that have been obtained thus far. Also discussed is the Gibbs phenomenon for spherical harmonic spectral methods applied to functions that are piecewise analytic on spheres. We prove that knowledge of the first N spherical harmonic coefficients yield an exponentially convergent approximation to a spherical piecewise smooth function, hence completely overcoming the Gibbs phenomenon. Higher order numerical methods are applied to a specific one-dimensional hyperbolic system that describes the shallow water dynamics of a linearly sloping gulf. This problem is challenging due to the constantly changing location of where the water touches the shore. At this point the equation loses its strong hyperbolicity, and conventional numerical methods may not produce the correct solution. Also, any discontinuities that may arise as a result of the nonlinearity cannot be predicted, and this must be considered in selecting a numerical method.
“DTIC ADA322928: Numerical Algorithms For Compressible Turbulence.” Metadata:
- Title: ➤ DTIC ADA322928: Numerical Algorithms For Compressible Turbulence.
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA322928: Numerical Algorithms For Compressible Turbulence.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Gottlieb, David - BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS - *ALGORITHMS - *TURBULENCE - SHALLOW WATER - COMPRESSIBLE FLOW - APPROXIMATION(MATHEMATICS) - PARTIAL DIFFERENTIAL EQUATIONS - CONVERGENCE - NUMERICAL METHODS AND PROCEDURES - APPLIED MATHEMATICS - ANALYTIC FUNCTIONS - FOURIER SERIES.
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- Internet Archive ID: DTIC_ADA322928
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16DTIC ADA343353: Numerical And Symbolic Algorithms For Application Specific Signal Processing
By Defense Technical Information Center
Our research under the RASSP program focussed on the development of new signal processing algorithms to exploit the advantages and opportunities of rapid prototyping for signal processing systems. Our work was carried out in the Research Laboratory of Electronics at MIT with close collaboration and interaction with industrial partners including Lockheed Sanders. Our primary accomplishments were in several categories. We developed and explored new classes of signals and algorithms related to chaotic behavior in nonlinear systems. We also developed and explored the use of fractal signals for communications. A third new nonlinear signal class that we explored exploits the solution behavior of certain nonlinear wave equations. A significant part of our effort was directed at the exploration of algorithm-based fault tolerant architectures for signal processing and for the use of approximate processing techniques which can be exploited in the contexts of low-power signal processing architectures and in other aspects of processor resource management. We also explored opportunities to exploit multirate signal processing. In the following section we briefly summarize our results in each of these areas. Section 3 contains a bibliography of the journal articles, book chapters, and conference papers in which the details of our work is presented.
“DTIC ADA343353: Numerical And Symbolic Algorithms For Application Specific Signal Processing” Metadata:
- Title: ➤ DTIC ADA343353: Numerical And Symbolic Algorithms For Application Specific Signal Processing
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA343353: Numerical And Symbolic Algorithms For Application Specific Signal Processing” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Oppenheim, Alan V. - MASSACHUSETTS INST OF TECH CAMBRIDGE RESEARCH LAB OF ELECTRONICS - *ALGORITHMS - *SIGNAL PROCESSING - FRACTALS - CHAOS - NONLINEAR SYSTEMS - COMMUNICATIONS NETWORKS - FAULT TOLERANCE - NONLINEAR ALGEBRAIC EQUATIONS - WAVE EQUATIONS - WAVELET TRANSFORMS.
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- Internet Archive ID: DTIC_ADA343353
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17[EuroPython 2014] Yves - Performance Python For Numerical Algorithms
Yves - Performance Python for Numerical Algorithms [EuroPython 2014] [23 July 2014] This talk is about several approaches to implement high performing numerical algorithms and applications in Python. It introduces into approaches like vectorization, multi-threading, parallelization (CPU/GPU), dynamic compiling, high throughput IO operations. The approach is a practical one in that every approach is illustrated by specific Python examples. ----- This talk is about several approaches to implement high performing numerical algorithms and applications in Python. It introduces into approaches like multi-threading, parallelization (CPU/GPU), dynamic compiling, high throughput IO operations. The approach is a practical one in that every approach is illustrated by specific Python examples. The talk uses, among others, the following libraries: * NumPy * numexpr * IPython.Parallel * Numba * NumbaPro * PyTables
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- Title: ➤ [EuroPython 2014] Yves - Performance Python For Numerical Algorithms
- Language: English
“[EuroPython 2014] Yves - Performance Python For Numerical Algorithms” Subjects and Themes:
- Subjects: ➤ dynamic compiling - performance - python - fast io - EuroPython2014 - Python
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- Internet Archive ID: EuroPython_2014_kryisH8a
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18The Emergence Of Gravitational Wave Science: 100 Years Of Development Of Mathematical Theory, Detectors, Numerical Algorithms, And Data Analysis Tools
By Michael Holst, Olivier Sarbach, Manuel Tiglio and Michele Vallisneri
On September 14, 2015, the newly upgraded Laser Interferometer Gravitational-wave Observatory (LIGO) recorded a loud gravitational-wave (GW) signal, emitted a billion light-years away by a coalescing binary of two stellar-mass black holes. The detection was announced in February 2016, in time for the hundredth anniversary of Einstein's prediction of GWs within the theory of general relativity (GR). The signal represents the first direct detection of GWs, the first observation of a black-hole binary, and the first test of GR in its strong-field, high-velocity, nonlinear regime. In the remainder of its first observing run, LIGO observed two more signals from black-hole binaries, one moderately loud, another at the boundary of statistical significance. The detections mark the end of a decades-long quest, and the beginning of GW astronomy: finally, we are able to probe the unseen, electromagnetically dark Universe by listening to it. In this article, we present a short historical overview of GW science: this young discipline combines GR, arguably the crowning achievement of classical physics, with record-setting, ultra-low-noise laser interferometry, and with some of the most powerful developments in the theory of differential geometry, partial differential equations, high-performance computation, numerical analysis, signal processing, statistical inference, and data science. Our emphasis is on the synergy between these disciplines, and how mathematics, broadly understood, has historically played, and continues to play, a crucial role in the development of GW science. We focus on black holes, which are very pure mathematical solutions of Einstein's gravitational-field equations that are nevertheless realized in Nature, and that provided the first observed signals.
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- Title: ➤ The Emergence Of Gravitational Wave Science: 100 Years Of Development Of Mathematical Theory, Detectors, Numerical Algorithms, And Data Analysis Tools
- Authors: Michael HolstOlivier SarbachManuel TiglioMichele Vallisneri
“The Emergence Of Gravitational Wave Science: 100 Years Of Development Of Mathematical Theory, Detectors, Numerical Algorithms, And Data Analysis Tools” Subjects and Themes:
- Subjects: ➤ Computational Physics - Data Analysis, Statistics and Probability - Physics - General Relativity and Quantum Cosmology - Instrumentation and Detectors - History and Philosophy of Physics
Edition Identifiers:
- Internet Archive ID: arxiv-1607.05251
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19DTIC ADA044903: Numerical Aspects Of Trajectory Algorithms For Nonlinearly Constrained Optimization.
By Defense Technical Information Center
This paper discusses two algorithms for nonlinearly constrained optimization. These algorithms -- the penalty and barrier trajectory algorithms -- are based on an examination of the trajectories of approach to the solution that characterize the quadratic penalty function and the logarithmic barrier function, respectively. Although closely related in principle, the two algorithms display important differences in their implementation as well as in the properties of the generated iterates. The discussion will emphasize the numerical aspects of implementation of the trajectory algorithms, with particular attention to the choice of reliable methods for carrying out the required computations. (Author)
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- Title: ➤ DTIC ADA044903: Numerical Aspects Of Trajectory Algorithms For Nonlinearly Constrained Optimization.
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA044903: Numerical Aspects Of Trajectory Algorithms For Nonlinearly Constrained Optimization.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Murray,Walter - STANFORD UNIV CALIF SYSTEMS OPTIMIZATION LAB - *DIFFERENTIAL EQUATIONS - *NONLINEAR PROGRAMMING - ALGORITHMS - NUMERICAL ANALYSIS - SOLUTIONS(GENERAL) - POLYNOMIALS - SEARCHING - TRAJECTORIES - ITERATIONS - LAGRANGIAN FUNCTIONS - MINIMAX TECHNIQUE
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- Internet Archive ID: DTIC_ADA044903
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20NASA Technical Reports Server (NTRS) 19870002109: Numerical Algorithms For Finite Element Computations On Concurrent Processors
By NASA Technical Reports Server (NTRS)
The work of several graduate students which relate to the NASA grant is briefly summarized. One student has worked on a detailed analysis of the so-called ijk forms of Gaussian elemination and Cholesky factorization on concurrent processors. Another student has worked on the vectorization of the incomplete Cholesky conjugate method on the CYBER 205. Two more students implemented various versions of Gaussian elimination and Cholesky factorization on the FLEX/32.
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- Title: ➤ NASA Technical Reports Server (NTRS) 19870002109: Numerical Algorithms For Finite Element Computations On Concurrent Processors
- Author: ➤ NASA Technical Reports Server (NTRS)
- Language: English
“NASA Technical Reports Server (NTRS) 19870002109: Numerical Algorithms For Finite Element Computations On Concurrent Processors” Subjects and Themes:
- Subjects: ➤ NASA Technical Reports Server (NTRS) - ALGORITHMS - COMPUTER TECHNIQUES - CONCURRENT PROCESSING - FINITE ELEMENT METHOD - CHOLESKY FACTORIZATION - CONJUGATE GRADIENT METHOD - GAUSSIAN ELIMINATION - POISSON EQUATION - STIFFNESS MATRIX - VECTOR ANALYSIS - Ortega, J. M.
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- Internet Archive ID: NASA_NTRS_Archive_19870002109
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21NASA Technical Reports Server (NTRS) 19960054188: Numerical Algorithms Based On Biorthogonal Wavelets
By NASA Technical Reports Server (NTRS)
Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.
“NASA Technical Reports Server (NTRS) 19960054188: Numerical Algorithms Based On Biorthogonal Wavelets” Metadata:
- Title: ➤ NASA Technical Reports Server (NTRS) 19960054188: Numerical Algorithms Based On Biorthogonal Wavelets
- Author: ➤ NASA Technical Reports Server (NTRS)
- Language: English
“NASA Technical Reports Server (NTRS) 19960054188: Numerical Algorithms Based On Biorthogonal Wavelets” Subjects and Themes:
- Subjects: ➤ NASA Technical Reports Server (NTRS) - PARTIAL DIFFERENTIAL EQUATIONS - INTEGRAL TRANSFORMATIONS - ALGORITHMS - RESOLUTION - NUMERICAL ANALYSIS - HYPOTHESES - ELLIPSES - WAVELET ANALYSIS - ORTHOGONALITY - BURGER EQUATION - Ponenti, Pj. - Liandrat, J.
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- Internet Archive ID: NASA_NTRS_Archive_19960054188
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22DTIC ADA309409: Numerical And Symbolic Algorithms For Application Specific Signal Processing.
By Defense Technical Information Center
During the period of this grant, our detailed technical accomplishments are reported through journal articles and technical reports. Each of our semi-annual reports will highlight certain technical areas and provide a summary listing of our technical articles related to the project.
“DTIC ADA309409: Numerical And Symbolic Algorithms For Application Specific Signal Processing.” Metadata:
- Title: ➤ DTIC ADA309409: Numerical And Symbolic Algorithms For Application Specific Signal Processing.
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA309409: Numerical And Symbolic Algorithms For Application Specific Signal Processing.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Oppenheim, Alan V. - MASSACHUSETTS INST OF TECH CAMBRIDGE RESEARCH LAB OF ELECTRONICS - *ALGORITHMS - *SIGNAL PROCESSING - COMPUTERIZED SIMULATION - OPTIMIZATION - DISTRIBUTED DATA PROCESSING - COMPUTER COMMUNICATIONS - CHAOS - SIGNAL TO NOISE RATIO - COMMUNICATIONS NETWORKS - FAST FOURIER TRANSFORMS - SYSTEMS ANALYSIS - DYNAMIC PROGRAMMING - FAULT TOLERANT COMPUTING - NONLINEAR PROGRAMMING - SYMBOLIC PROGRAMMING - PACKET SWITCHING.
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- Internet Archive ID: DTIC_ADA309409
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23Numerical Algorithms Based On Galerkin Methods For The Modeling Of Reactive Interfaces In Photoelectrochemical (PEC) Solar Cells
By Michael Harmon, Irene M. Gamba and Kui Ren
This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive semiconductor and electrolyte interfaces. We present three numerical algorithms, mainly based on a mixed finite element and a local discontinuous Galerkin method for spatial discretization, with carefully chosen numerical fluxes, and implicit-explicit time stepping techniques, for solving the time-dependent nonlinear systems of partial differential equations. We perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model.
“Numerical Algorithms Based On Galerkin Methods For The Modeling Of Reactive Interfaces In Photoelectrochemical (PEC) Solar Cells” Metadata:
- Title: ➤ Numerical Algorithms Based On Galerkin Methods For The Modeling Of Reactive Interfaces In Photoelectrochemical (PEC) Solar Cells
- Authors: Michael HarmonIrene M. GambaKui Ren
“Numerical Algorithms Based On Galerkin Methods For The Modeling Of Reactive Interfaces In Photoelectrochemical (PEC) Solar Cells” Subjects and Themes:
- Subjects: Computational Physics - Physics - Numerical Analysis - Computing Research Repository - Mathematics
Edition Identifiers:
- Internet Archive ID: arxiv-1604.07855
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24Comparison Of Several Numerical Algorithms With The Use Of Predictor And Corrector For Solving Ode
By Subhashini | Srividhya. B
In this paper, we introduce various numerical methods for the solutions of ordinary differential equations and its application. We consider the Taylor series, Runge Kutta, Euler's methods problem to solve the Adam's Predictor, Corrector and Milne's Predictor, Corrector to get the exact solution and the approximate solution. by Subhashini | Srividhya. B "Comparison of Several Numerical Algorithms with the use of Predictor and Corrector for solving ode" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29318.pdf Paper URL: https://www.ijtsrd.com/mathemetics/other/29318/comparison-of-several-numerical-algorithms-with-the-use-of-predictor-and-corrector-for-solving-ode/subhashini
“Comparison Of Several Numerical Algorithms With The Use Of Predictor And Corrector For Solving Ode” Metadata:
- Title: ➤ Comparison Of Several Numerical Algorithms With The Use Of Predictor And Corrector For Solving Ode
- Author: Subhashini | Srividhya. B
- Language: English
“Comparison Of Several Numerical Algorithms With The Use Of Predictor And Corrector For Solving Ode” Subjects and Themes:
- Subjects: Ordinary differential equation - Initial Condition - Adams Predictor - Corrector and Milne's Predictor - Corrector
Edition Identifiers:
- Internet Archive ID: ➤ httpswww.ijtsrd.commathemeticsother29318comparison-of-several-numerical-algorith
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25DTIC ADA288202: Numerical And Symbolic Algorithms For Application Specific Signal Processing.
By Defense Technical Information Center
Work by Prof. Oppenheim and his collaborators is summarized here. The first step in one aspect of our research in the RASSP program involves evaluating the abilities and limitations of current DSP system design tools. We are concerned with what algorithms the tools support, and how the tool abilities might be expanded in the future to support emerging signal processing techniques. Major accomplishments in our recent approximate processing research include: (1) conceptual and mathematical elaboration of approximate process- ing concepts, (2) formulation and implementation of a class of incremental refinement algorithms for the short-time Fourier transform, (3) illustration of design issues in the context of incremental refinement algorithms , (4) continued development of the IPUS-C++ software environment for supporting the design of application systems with embedded approximate signal processing capabilities, and (5) initiation of a project to build a software environment to support algorithm design for approximate signal processing.
“DTIC ADA288202: Numerical And Symbolic Algorithms For Application Specific Signal Processing.” Metadata:
- Title: ➤ DTIC ADA288202: Numerical And Symbolic Algorithms For Application Specific Signal Processing.
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA288202: Numerical And Symbolic Algorithms For Application Specific Signal Processing.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Oppenheim, Alan V. - MASSACHUSETTS INST OF TECH CAMBRIDGE RESEARCH LAB OF ELECTRONICS - *ALGORITHMS - *SIGNAL PROCESSING - *SOFTWARE ENGINEERING - COMPUTER PROGRAMS - FRACTALS - AVIONICS - REENTRY VEHICLES - COMPUTERIZED SIMULATION - INFRARED DETECTION - FOURIER TRANSFORMATION - PROGRAMMING LANGUAGES.
Edition Identifiers:
- Internet Archive ID: DTIC_ADA288202
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26Numerical Algorithms For 1-d Backward Stochastic Differential Equations: Convergence And Simulations
By Shige Peng and Mingyu Xu
In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.
“Numerical Algorithms For 1-d Backward Stochastic Differential Equations: Convergence And Simulations” Metadata:
- Title: ➤ Numerical Algorithms For 1-d Backward Stochastic Differential Equations: Convergence And Simulations
- Authors: Shige PengMingyu Xu
- Language: English
Edition Identifiers:
- Internet Archive ID: arxiv-math0611864
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27Numerical Algorithms For A Variational Problem Of The Spatial Segregation Of Reaction-Diffusion Systems
In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.
“Numerical Algorithms For A Variational Problem Of The Spatial Segregation Of Reaction-Diffusion Systems” Metadata:
- Title: ➤ Numerical Algorithms For A Variational Problem Of The Spatial Segregation Of Reaction-Diffusion Systems
Edition Identifiers:
- Internet Archive ID: arxiv-1206.1388
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28NASA Technical Reports Server (NTRS) 20040090584: Numerical Roll Reversal Predictor Corrector Aerocapture And Precision Landing Guidance Algorithms For The Mars Surveyor Program 2001 Missions
By NASA Technical Reports Server (NTRS)
This paper describes the development and evaluation of a numerical roll reversal predictor-corrector guidance algorithm for the atmospheric flight portion of the Mars Surveyor Program 2001 Orbiter and Lander missions. The Lander mission utilizes direct entry and has a demanding requirement to deploy its parachute within 10 km of the target deployment point. The Orbiter mission utilizes aerocapture to achieve a precise captured orbit with a single atmospheric pass. Detailed descriptions of these predictor-corrector algorithms are given. Also, results of three and six degree-of-freedom Monte Carlo simulations which include navigation, aerodynamics, mass properties and atmospheric density uncertainties are presented.
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- Title: ➤ NASA Technical Reports Server (NTRS) 20040090584: Numerical Roll Reversal Predictor Corrector Aerocapture And Precision Landing Guidance Algorithms For The Mars Surveyor Program 2001 Missions
- Author: ➤ NASA Technical Reports Server (NTRS)
- Language: English
“NASA Technical Reports Server (NTRS) 20040090584: Numerical Roll Reversal Predictor Corrector Aerocapture And Precision Landing Guidance Algorithms For The Mars Surveyor Program 2001 Missions” Subjects and Themes:
- Subjects: ➤ NASA Technical Reports Server (NTRS) - AEROCAPTURE - AIRCRAFT GUIDANCE - AIRCRAFT LANDING - ALGORITHMS - MARS SURVEYOR 2001 MISSION - PREDICTOR-CORRECTOR METHODS - MARS ATMOSPHERE - ATMOSPHERIC DENSITY - DEGREES OF FREEDOM - DYNAMIC PRESSURE - MONTE CARLO METHOD - LIFT DRAG RATIO - NAVIGATION - Powell, Richard W.
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- Internet Archive ID: NASA_NTRS_Archive_20040090584
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29DTIC ADA099562: Research On Numerical Algorithms For The Three-Dimensional Navier-Stokes Equations. II. Dissipative Finite Element.
By Defense Technical Information Center
The objective of this research project is to derive and evaluate versatile, accurate and efficient numerical algorithms for solution of aerodynamic flowfields at large Reynolds number. The concept of a dissipative finite element algorithm has been refined and extended to solution of a complete equation set in aerodynamics. The resultant numerical results are highly encouraging with respect to shock resolution and overall performance, utilizing both a linear quadratic finite element embodiment of the theory. The theoretical formulational statement of the algorithm has been extended to a multi-dimensional description in generalized coordinates. The key efficiency feature is identification of the tensor matrix resolution of the Jacobian of the Newton algorithm for this statement. The concept of application of the continuity equation solution, as a differential constraint on the momentum equation algorithm, has been validated. The formulation is directly useful for viscous marching procedures, and with some modifications could be equally useful for a low Mach number Navier - Stokes solution algorithm. (Author)
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- Title: ➤ DTIC ADA099562: Research On Numerical Algorithms For The Three-Dimensional Navier-Stokes Equations. II. Dissipative Finite Element.
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA099562: Research On Numerical Algorithms For The Three-Dimensional Navier-Stokes Equations. II. Dissipative Finite Element.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Baker,A J - TENNESSE UNIV KNOXVILLE DEPT OF ENGINEERING SCIENCE AND MECHANICS - *FINITE ELEMENT ANALYSIS - *NAVIER STOKES EQUATIONS - *THREE DIMENSIONAL FLOW - KINEMATICS - ALGORITHMS - DISSIPATION - SOLUTIONS(GENERAL) - MACH NUMBER - NUMERICAL METHODS AND PROCEDURES - REYNOLDS NUMBER - AERODYNAMICS - SHOCK TUBES
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- Internet Archive ID: DTIC_ADA099562
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30DTIC ADA093617: A Numerical Investigation Of Ellipsoid Algorithms For Large-Scale Linear Programming.
By Defense Technical Information Center
The ellipsoid algorithm associated with Shor, Khachiyan and others has certain theoretical properties that suggest its use as a linear programming algorithm. Some of the practical difficulties are investigated here. A variant of the ellipsoid update is first developed, to take advantage of the range constraints that often occur in linear programs (i.e., constraints of the form l or = aTx or = u, where u - l is reasonably small). Methods for storing the ellipsoid matrix are then discussed for both dense and sparse problems. In the large-scale case, a major difficulty is that the desired ellipsoid cannot be represented compactly throughout an arbitrary number of iterations. Some schemes are suggested for economizing on storage, but any guarantee of convergence is effectively lost. At this stage there remains little room for optimism that an ellipsoid-based algorithm could complete with the simplex method on problems with a large number of variables. (Author)
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- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA093617: A Numerical Investigation Of Ellipsoid Algorithms For Large-Scale Linear Programming.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Gill,Philip E - STANFORD UNIV CA SYSTEMS OPTIMIZATION LAB - *LINEAR PROGRAMMING - *ELLIPSOIDS - ALGORITHMS - MATRICES(MATHEMATICS) - GRAPHS - NUMERICAL ANALYSIS - EIGENVALUES - TRANSFORMATIONS(MATHEMATICS) - SPARSE MATRIX - CONVEX SETS - SIMPLEX METHOD
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- Internet Archive ID: DTIC_ADA093617
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31DTIC ADA223476: The Development And Evaluation Of Numerical Algorithms For MIMD Computers
By Defense Technical Information Center
Two activities were pursued under this grant. The first was a visitor program to conduct research on numerical algorithms for MIMD computers. The program is summarized in the following attachments. Attachment A - List of Researchers Supported; Attachment B - List of Reports Completed; and Attachment C - Reports. The second activity was a workshop on the Control of fluid Dynamic Systems held on March 28-29, 1989. The workshop is summarized in attachments. Attachment D - Workshop Summary; and Attachment E - List of Workshop Participants.
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- Title: ➤ DTIC ADA223476: The Development And Evaluation Of Numerical Algorithms For MIMD Computers
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA223476: The Development And Evaluation Of Numerical Algorithms For MIMD Computers” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Voigt, Robert G - NATIONAL AERONAUTICS AND SPACE ADMIN LANGLEY RESEARCH CENTER HAMPTON VA - *ALGORITHMS - *COMPUTERS - ATTACHMENT - FLUID DYNAMICS
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- Internet Archive ID: DTIC_ADA223476
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32DTIC ADA435543: Constant And Power-of-2 Segmentation Algorithms For A High Speed Numerical Function Generator
By Defense Technical Information Center
The realization of high-speed numeric computation is a sought-after commodity for real world applications, including high-speed scientific computation, digital signal processing, and embedded computers. An example of this is the generation of elementary functions, such as sin( ) x , x e and log( ) x . Sasao, Butler and Reidel Ref. 1 developed a high speed numeric function generator using a look-up table (LUT) cascade. Their method used a piecewise linear segmentation algorithm to generate the functions Ref. 1. In this thesis, two alternative segmentation algorithms are proposed and compared to the results of Sasao, Butler and Reidel Ref.1. The first algorithm is the Constant Approximation. This algorithm uses lines of slope zero to approximate a curve. The second algorithm is the power-of-2-approximation. This method uses 2i x to approximate a curve. The constant approximation eliminates the need for a multiplier and adder, while the power-of-2-approximations eliminates the need for multiplier, thus improving the computation speed. Tradeoffs between the three methods are examined. Specifically, the implementation of the piecewise linear algorithm requires the most amount of hardware and is slower than the other two. The advantage that it has is that it yields the least amount of segments to generate a function. The constant approximation requires the most amount of hardware to realize a function, but is the fastest implementation. The power-of-2 approximation is an intermediate choice that balances speed and hardware requirements.
“DTIC ADA435543: Constant And Power-of-2 Segmentation Algorithms For A High Speed Numerical Function Generator” Metadata:
- Title: ➤ DTIC ADA435543: Constant And Power-of-2 Segmentation Algorithms For A High Speed Numerical Function Generator
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA435543: Constant And Power-of-2 Segmentation Algorithms For A High Speed Numerical Function Generator” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Valenzuela, Zaldy M - NAVAL POSTGRADUATE SCHOOL MONTEREY CA - *ALGORITHMS - *NUMERICAL ANALYSIS - VELOCITY - SIGNAL PROCESSING - LINEAR SYSTEMS - FUNCTIONS - REQUIREMENTS - DIGITAL SYSTEMS - COMPUTERS - THESES - EMBEDDING - TABLES(DATA) - TRADE OFF ANALYSIS - BALANCES
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- Internet Archive ID: DTIC_ADA435543
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33Constrained Transport Algorithms For Numerical Relativity. I. Development Of A Finite Difference Scheme
By David L. Meier
A scheme is presented for accurately propagating the gravitational field constraints in finite difference implementations of numerical relativity. The method is based on similar techniques used in astrophysical magnetohydrodynamics and engineering electromagnetics, and has properties of a finite differential calculus on a four-dimensional manifold. It is motivated by the arguments that 1) an evolutionary scheme that naturally satisfies the Bianchi identities will propagate the constraints, and 2) methods in which temporal and spatial derivatives commute will satisfy the Bianchi identities implicitly. The proposed algorithm exactly propagates the constraints in a local Riemann normal coordinate system; {\it i.e.}, all terms in the Bianchi identities (which all vary as $\partial^3 g$) cancel to machine roundoff accuracy at each time step. In a general coordinate basis, these terms, and those that vary as $\partial g\partial^2 g$, also can be made to cancel, but differences of connection terms, proportional to $(\partial g)^3$, will remain, resulting in a net truncation error. Detailed and complex numerical experiments with four-dimensional staggered grids will be needed to completely examine the stability and convergence properties of this method. If such techniques are successful for finite difference implementations of numerical relativity, other implementations, such as finite element (and eventually pseudo-spectral) techniques, might benefit from schemes that use four-dimensional grids and that have temporal and spatial derivatives that commute.
“Constrained Transport Algorithms For Numerical Relativity. I. Development Of A Finite Difference Scheme” Metadata:
- Title: ➤ Constrained Transport Algorithms For Numerical Relativity. I. Development Of A Finite Difference Scheme
- Author: David L. Meier
- Language: English
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- Internet Archive ID: arxiv-astro-ph0312052
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34User Manual - Numerical Algorithms Group
A scheme is presented for accurately propagating the gravitational field constraints in finite difference implementations of numerical relativity. The method is based on similar techniques used in astrophysical magnetohydrodynamics and engineering electromagnetics, and has properties of a finite differential calculus on a four-dimensional manifold. It is motivated by the arguments that 1) an evolutionary scheme that naturally satisfies the Bianchi identities will propagate the constraints, and 2) methods in which temporal and spatial derivatives commute will satisfy the Bianchi identities implicitly. The proposed algorithm exactly propagates the constraints in a local Riemann normal coordinate system; {\it i.e.}, all terms in the Bianchi identities (which all vary as $\partial^3 g$) cancel to machine roundoff accuracy at each time step. In a general coordinate basis, these terms, and those that vary as $\partial g\partial^2 g$, also can be made to cancel, but differences of connection terms, proportional to $(\partial g)^3$, will remain, resulting in a net truncation error. Detailed and complex numerical experiments with four-dimensional staggered grids will be needed to completely examine the stability and convergence properties of this method. If such techniques are successful for finite difference implementations of numerical relativity, other implementations, such as finite element (and eventually pseudo-spectral) techniques, might benefit from schemes that use four-dimensional grids and that have temporal and spatial derivatives that commute.
“User Manual - Numerical Algorithms Group” Metadata:
- Title: ➤ User Manual - Numerical Algorithms Group
“User Manual - Numerical Algorithms Group” Subjects and Themes:
- Subjects: manualzilla - manuals
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- Internet Archive ID: manualzilla-id-5825135
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35NASA Technical Reports Server (NTRS) 20100024459: Stochastic Formal Correctness Of Numerical Algorithms
By NASA Technical Reports Server (NTRS)
We provide a framework to bound the probability that accumulated errors were never above a given threshold on numerical algorithms. Such algorithms are used for example in aircraft and nuclear power plants. This report contains simple formulas based on Levy's and Markov's inequalities and it presents a formal theory of random variables with a special focus on producing concrete results. We selected four very common applications that fit in our framework and cover the common practices of systems that evolve for a long time. We compute the number of bits that remain continuously significant in the first two applications with a probability of failure around one out of a billion, where worst case analysis considers that no significant bit remains. We are using PVS as such formal tools force explicit statement of all hypotheses and prevent incorrect uses of theorems.
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- Title: ➤ NASA Technical Reports Server (NTRS) 20100024459: Stochastic Formal Correctness Of Numerical Algorithms
- Author: ➤ NASA Technical Reports Server (NTRS)
- Language: English
“NASA Technical Reports Server (NTRS) 20100024459: Stochastic Formal Correctness Of Numerical Algorithms” Subjects and Themes:
- Subjects: ➤ NASA Technical Reports Server (NTRS) - ALGORITHMS - PROBABILITY THEORY - RANDOM VARIABLES - HYPOTHESES - STOCHASTIC PROCESSES - THEOREMS - INEQUALITIES - PROCEDURES - FAILURE - ERRORS - ACCUMULATIONS - Daumas, Marc - Lester, David - Martin-Dorel, Erik - Truffert, Annick
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- Internet Archive ID: NASA_NTRS_Archive_20100024459
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36NASA Technical Reports Server (NTRS) 19840014530: Dynamics Analysis Of Electrodynamic Satellite Tethers. Equations Of Motion And Numerical Solution Algorithms For The Tether
By NASA Technical Reports Server (NTRS)
The equations of motion are developed for a perfectly flexible, inelastic tether with a satellite at its extremity. The tether is attached to a space vehicle in orbit. The tether is allowed to possess electrical conductivity. A numerical solution algorithm to provide the motion of the tether and satellite system is presented. The resulting differential equations can be solved by various existing standard numerical integration computer programs. The resulting differential equations allow the introduction of approximations that can lead to analytical, approximate general solutions. The differential equations allow more dynamical insight of the motion.
“NASA Technical Reports Server (NTRS) 19840014530: Dynamics Analysis Of Electrodynamic Satellite Tethers. Equations Of Motion And Numerical Solution Algorithms For The Tether” Metadata:
- Title: ➤ NASA Technical Reports Server (NTRS) 19840014530: Dynamics Analysis Of Electrodynamic Satellite Tethers. Equations Of Motion And Numerical Solution Algorithms For The Tether
- Author: ➤ NASA Technical Reports Server (NTRS)
- Language: English
“NASA Technical Reports Server (NTRS) 19840014530: Dynamics Analysis Of Electrodynamic Satellite Tethers. Equations Of Motion And Numerical Solution Algorithms For The Tether” Subjects and Themes:
- Subjects: ➤ NASA Technical Reports Server (NTRS) - COMPUTERIZED SIMULATION - DIFFERENTIAL EQUATIONS - ELECTRICAL PROPERTIES - EQUATIONS OF MOTION - TETHERED SATELLITES - TETHERING - TETHERLINES - ALGORITHMS - ANGULAR MOMENTUM - BOUNDARY VALUE PROBLEMS - ELASTIC PROPERTIES - FLEXIBILITY - Nacozy, P. E.
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- Internet Archive ID: NASA_NTRS_Archive_19840014530
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37NASA Technical Reports Server (NTRS) 19860020953: On Substructuring Algorithms And Solution Techniques For The Numerical Approximation Of Partial Differential Equations
By NASA Technical Reports Server (NTRS)
Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.
“NASA Technical Reports Server (NTRS) 19860020953: On Substructuring Algorithms And Solution Techniques For The Numerical Approximation Of Partial Differential Equations” Metadata:
- Title: ➤ NASA Technical Reports Server (NTRS) 19860020953: On Substructuring Algorithms And Solution Techniques For The Numerical Approximation Of Partial Differential Equations
- Author: ➤ NASA Technical Reports Server (NTRS)
- Language: English
“NASA Technical Reports Server (NTRS) 19860020953: On Substructuring Algorithms And Solution Techniques For The Numerical Approximation Of Partial Differential Equations” Subjects and Themes:
- Subjects: ➤ NASA Technical Reports Server (NTRS) - ALGEBRA - LINEAR SYSTEMS - MATRICES (MATHEMATICS) - PARALLEL PROCESSING (COMPUTERS) - SUBSTRUCTURES - SYMMETRY - FINITE ELEMENT METHOD - GAUSSIAN ELIMINATION - HELMHOLTZ VORTICITY EQUATION - PARTIAL DIFFERENTIAL EQUATIONS - STOKES LAW (FLUID MECHANICS) - Gunzburger, M. D. - Nicolaides, R. A.
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- Internet Archive ID: NASA_NTRS_Archive_19860020953
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38NASA Technical Reports Server (NTRS) 19890007025: A Bibliography On Parallel And Vector Numerical Algorithms
By NASA Technical Reports Server (NTRS)
This is a bibliography on numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are also listed.
“NASA Technical Reports Server (NTRS) 19890007025: A Bibliography On Parallel And Vector Numerical Algorithms” Metadata:
- Title: ➤ NASA Technical Reports Server (NTRS) 19890007025: A Bibliography On Parallel And Vector Numerical Algorithms
- Author: ➤ NASA Technical Reports Server (NTRS)
- Language: English
“NASA Technical Reports Server (NTRS) 19890007025: A Bibliography On Parallel And Vector Numerical Algorithms” Subjects and Themes:
- Subjects: ➤ NASA Technical Reports Server (NTRS) - ALGORITHMS - NUMERICAL ANALYSIS - PARALLEL PROCESSING (COMPUTERS) - VECTOR ANALYSIS - APPLICATIONS PROGRAMS (COMPUTERS) - ARCHITECTURE (COMPUTERS) - PROGRAMMING LANGUAGES - Ortega, James M. - Voigt, Robert G. - Romine, Charles H.
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- Internet Archive ID: NASA_NTRS_Archive_19890007025
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39NASA Technical Reports Server (NTRS) 19960020541: Numerical Algorithms Based On Biorthogonal Wavelets
By NASA Technical Reports Server (NTRS)
Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.
“NASA Technical Reports Server (NTRS) 19960020541: Numerical Algorithms Based On Biorthogonal Wavelets” Metadata:
- Title: ➤ NASA Technical Reports Server (NTRS) 19960020541: Numerical Algorithms Based On Biorthogonal Wavelets
- Author: ➤ NASA Technical Reports Server (NTRS)
- Language: English
“NASA Technical Reports Server (NTRS) 19960020541: Numerical Algorithms Based On Biorthogonal Wavelets” Subjects and Themes:
- Subjects: ➤ NASA Technical Reports Server (NTRS) - WAVELET ANALYSIS - ALGORITHMS - BURGER EQUATION - OPERATORS (MATHEMATICS) - ELLIPTIC DIFFERENTIAL EQUATIONS - FOURIER TRANSFORMATION - PARABOLIC DIFFERENTIAL EQUATIONS - Ponenti, Pj. - Liandrat, J.
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- Internet Archive ID: NASA_NTRS_Archive_19960020541
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40NASA Technical Reports Server (NTRS) 20030112277: Algorithms For The Fractional Calculus: A Selection Of Numerical Methods
By NASA Technical Reports Server (NTRS)
Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.
“NASA Technical Reports Server (NTRS) 20030112277: Algorithms For The Fractional Calculus: A Selection Of Numerical Methods” Metadata:
- Title: ➤ NASA Technical Reports Server (NTRS) 20030112277: Algorithms For The Fractional Calculus: A Selection Of Numerical Methods
- Author: ➤ NASA Technical Reports Server (NTRS)
- Language: English
“NASA Technical Reports Server (NTRS) 20030112277: Algorithms For The Fractional Calculus: A Selection Of Numerical Methods” Subjects and Themes:
- Subjects: ➤ NASA Technical Reports Server (NTRS) - ALGORITHMS - NUMERICAL ANALYSIS - CALCULUS - DIFFERENTIAL EQUATIONS - MATHEMATICAL MODELS - DIFFUSION - ELECTROCHEMISTRY - VISCOELASTICITY - MEASURE AND INTEGRATION - INTEGRALS - Diethelm, K. - Ford, N. J. - Freed, A. D. - Luchko, Yu.
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- Internet Archive ID: NASA_NTRS_Archive_20030112277
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41Analytical And Numerical Flash-Algorithms For Track Fits
By M. Dima
Flash-algorithm track-reconstruction routines with speed factors 3000-4000 in excess those of traditional iterative routines are presented. The methods were successfully tested in the alignment of the Test Beam setup for the ATLAS Pixel Detector MCM-D modules yielding a 60 fold increase in alignment resolution over iterative routines, for the same amount of alocated CPU time.
“Analytical And Numerical Flash-Algorithms For Track Fits” Metadata:
- Title: ➤ Analytical And Numerical Flash-Algorithms For Track Fits
- Author: M. Dima
- Language: English
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- Internet Archive ID: arxiv-hep-ex0002021
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42Quasi-local Update Algorithms For Numerical Simulations Of D=3 SU(2) LGT In The Dual Formulation
By N. D. Hari Dass
In the dual formulation of d=3 SU(2) LGT, the link variables are group representations and valid configurations are those satisfying a number of triangle inequalities. In \cite{lat99} algorithms for local updates that automatically respect these constraints were described. It was also pointed out there that these local updates were not ergodic. In this presentation, we describe two different quasi-local updating algorithms which, in conjunction with the local updates, appear to be ergodic.
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- Title: ➤ Quasi-local Update Algorithms For Numerical Simulations Of D=3 SU(2) LGT In The Dual Formulation
- Author: N. D. Hari Dass
- Language: English
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- Internet Archive ID: arxiv-hep-lat0011047
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43Accurate Numerical Algorithms : A Collection Of Research Papers
In the dual formulation of d=3 SU(2) LGT, the link variables are group representations and valid configurations are those satisfying a number of triangle inequalities. In \cite{lat99} algorithms for local updates that automatically respect these constraints were described. It was also pointed out there that these local updates were not ergodic. In this presentation, we describe two different quasi-local updating algorithms which, in conjunction with the local updates, appear to be ergodic.
“Accurate Numerical Algorithms : A Collection Of Research Papers” Metadata:
- Title: ➤ Accurate Numerical Algorithms : A Collection Of Research Papers
- Language: English
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- Internet Archive ID: isbn_3540514775
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44DTIC ADA157525: Numerical Algorithms And Mathematical Software For Linear Control And Estimation Theory.
By Defense Technical Information Center
Research concentrated on designing and implementing a microprocessor based concurrent computing environment consisting of a number of Intel microprocessors with IEEE floating point arithmetic implemented in hardware. The major focus of our work was the design of a concurrent tasker in software to locate code can data, monitor computation and communication and report results to the user. The construction of viable numerical algebra modules in an IEEE floating point arithmetic was and continues to be part of the research. (Author)
“DTIC ADA157525: Numerical Algorithms And Mathematical Software For Linear Control And Estimation Theory.” Metadata:
- Title: ➤ DTIC ADA157525: Numerical Algorithms And Mathematical Software For Linear Control And Estimation Theory.
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA157525: Numerical Algorithms And Mathematical Software For Linear Control And Estimation Theory.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Klema,V - MASSACHUSETTS INST OF TECH CAMBRIDGE STATISTICS CENTER - *ALGORITHMS - *MATHEMATICAL PROGRAMMING - COMPUTER PROGRAMS - LINEAR SYSTEMS - CONTROL - MICROPROCESSORS - THEORY - ESTIMATES - ARITHMETIC - FLOATING POINT OPERATION
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- Internet Archive ID: DTIC_ADA157525
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45DTIC ADA315262: Fast Numerical Algorithms & SAR Applications.
By Defense Technical Information Center
Several fast signal processing algorithms applicable in target detection and recognition techniques have been developed. These include a novel accurate and efficient method for replacing IIR filters by FIR filters, a method for multiresolution implementation of operators via filter banks, a multiresolution strategy for numerical homogenization and an algorithm for Unequally Spaced Fast Fourier Transform (USFFT) in multiple dimensions. The USFFT algorithm was one of the specific goals of the proposal. This algorithm was shown to be about 20% more efficient than the previous approach. It was also used as a part of a code for computing antenna far field patterns from near field measurements.
“DTIC ADA315262: Fast Numerical Algorithms & SAR Applications.” Metadata:
- Title: ➤ DTIC ADA315262: Fast Numerical Algorithms & SAR Applications.
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA315262: Fast Numerical Algorithms & SAR Applications.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Beylkin, Gregory - COLORADO UNIV AT BOULDER DEPT OF APPLIED MATHEMATICS - *ALGORITHMS - *SIGNAL PROCESSING - *SYNTHETIC APERTURE RADAR - *FAST FOURIER TRANSFORMS - *RADAR SIGNALS - MEASUREMENT - TARGET RECOGNITION - NUMERICAL ANALYSIS - ACCURACY - EFFICIENCY - FAR FIELD - PARTIAL DIFFERENTIAL EQUATIONS - FILTERS - TARGET DETECTION - ANTENNA RADIATION PATTERNS - NEAR FIELD - HOMOGENEITY.
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- Internet Archive ID: DTIC_ADA315262
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46DTIC ADA195502: Concurrent Algorithms For Numerical Computation On Hypercube Computer.
By Defense Technical Information Center
The purpose of this grant was to purchase a hypercube computer to support DoD-sponsored research, and other research, in parallel numerical computation. The plans that were outlined in the proposal were followed very closely. We have purchased a 32-node Intel iPSC-D5 hypercube computer with the funds from this grant, and have used the matching University contribution to support the maintenance of this computer. This computer has been used, over the past year, for research in parallel numerical computation in areas including global optimization, VLSI design, large sparse systems of linear equations, and eigenvalue problems, as well as for research in the languages for parallel computation and in the debugging and measurement of parallel programs.
“DTIC ADA195502: Concurrent Algorithms For Numerical Computation On Hypercube Computer.” Metadata:
- Title: ➤ DTIC ADA195502: Concurrent Algorithms For Numerical Computation On Hypercube Computer.
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA195502: Concurrent Algorithms For Numerical Computation On Hypercube Computer.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Schnabel, R - COLORADO UNIV AT BOULDER DEPT OF COMPUTER SCIENCE - *PARALLEL PROCESSORS - *SUPERCONDUCTORS - COMPUTATIONS - DEPARTMENT OF DEFENSE - EIGENVALUES - GLOBAL - LINEAR ALGEBRAIC EQUATIONS - MEASUREMENT - NUMERICAL METHODS AND PROCEDURES - OPTIMIZATION
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- Internet Archive ID: DTIC_ADA195502
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47DTIC ADA162221: Numerical Algorithms & Parallel Tasking.
By Defense Technical Information Center
The long term goals of this research activity are derived from concurrent computing with emphasis on numerical algorithms that support a variety of scientific applications. Among the applications of immediate interest are signal processing, high statistical methods such as the bootstrap. The shorter term focus has been the refinement and enhancement of the concurrent computing environment itself and the numerical algorithms that form the foundation for the applications. The computer systems that support this research use hardware manufactured by Intel -- with the 8086 cpu and the 8087 floating point processor at the heart of each node. The nodes are contained in workstations (with up to seven Workers and a Manager in a workstation) that can operate independently or can be linked together during execution. Worker structure and memory are configurable to support experiments conducted in the course of this research. Keywords: Parallel processing; Synchronization(electronics).
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- Title: ➤ DTIC ADA162221: Numerical Algorithms & Parallel Tasking.
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA162221: Numerical Algorithms & Parallel Tasking.” Subjects and Themes:
- Subjects: ➤ DTIC Archive - Kelma,Virginia - MASSACHUSETTS INST OF TECH CAMBRIDGE - *ALGORITHMS - *DATA PROCESSING - SIGNAL PROCESSING - COMPUTATIONS - ENVIRONMENTS - COMPUTERS - PARALLEL PROCESSING - CONFIGURATIONS - SYNCHRONIZATION(ELECTRONICS) - STATISTICAL PROCESSES - DUAL MODE - FLOATING POINT OPERATION - COMPUTER OPERATORS
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- Internet Archive ID: DTIC_ADA162221
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48DTIC ADA581076: Numerical Algorithms For The Analysis Of Expert Opinions Elicited In Text Format
By Defense Technical Information Center
Latent Dirichlet Allocation (LDA) is a scheme which may be used to estimate topics and their probabilities within a corpus of text data. The fundamental assumptions in this scheme are that text is a realisation of a stochastic generative model and that this model is well described by the combination of multinomial probability distributions and Dirichlet probability distributions. Various means can be used to solve the Bayesian estimation task arising in LDA. Our formulations of LDA are applied to subject matter expert text data elicited through carefully constructed decision support workshops. In the main these workshops address substantial problems in Australian Defence Capability. The application of LDA here is motivated by a need to provide insights into the collected text, which is often voluminous and complex in form. Additional investigations described in this report concern questions of identifying and quantifying di erences between stake-holder group text written to a common subject matter. Sentiment scores and key-phase estimators are used to indicate stake-holder di erences. Some examples are provided using unclassi ed data.
“DTIC ADA581076: Numerical Algorithms For The Analysis Of Expert Opinions Elicited In Text Format” Metadata:
- Title: ➤ DTIC ADA581076: Numerical Algorithms For The Analysis Of Expert Opinions Elicited In Text Format
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA581076: Numerical Algorithms For The Analysis Of Expert Opinions Elicited In Text Format” Subjects and Themes:
- Subjects: ➤ DTIC Archive - DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION (AUSTRALIA) JOINT OPERATIONS DIVISION - *ALGORITHMS - *DATA MINING - *NUMERICAL ANALYSIS - *TEXT PROCESSING - AUSTRALIA - BAYES THEOREM - DECISION SUPPORT SYSTEMS - ESTIMATES - FORMULATIONS - MONTE CARLO METHOD - NATURAL LANGUAGE - PROBABILITY - PROBABILITY DISTRIBUTION FUNCTIONS - STOCHASTIC PROCESSES
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- Internet Archive ID: DTIC_ADA581076
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49DTIC ADA586691: Towards High Resolution Numerical Algorithms For Wave Dominated Physical Phenomena
By Defense Technical Information Center
During this project several new numerical algorithms were designed, analyzed, and implemented with the goal of accelerating computational experiments in time-domain electromagnetics and acoustics. Novel results include a new family of radiation boundary conditions used for truncating computational domains used in external scattering simulations. A new filter and also local time stepping method were created for stabilizing coarse temporal approximations for discontinuous Galerkin time-domain computations. In additional work a new tiling algorithm was developed allowing large numbers of polyomino tiles to be arranged to cover a two dimensional shape without leaving gaps. This abstract algorithm has application in the design of passive array antenna to minimize side-lobe radiation.
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- Title: ➤ DTIC ADA586691: Towards High Resolution Numerical Algorithms For Wave Dominated Physical Phenomena
- Author: ➤ Defense Technical Information Center
- Language: English
“DTIC ADA586691: Towards High Resolution Numerical Algorithms For Wave Dominated Physical Phenomena” Subjects and Themes:
- Subjects: ➤ DTIC Archive - RICE UNIV HOUSTON TX DEPT OF COMPUTATIONAL AND APPLIED MATHEMATICS - *ELECTROMAGNETIC RADIATION - *TIME DOMAIN - ACOUSTICS - ANTENNA ARRAYS - COMPUTATIONS - ELECTROMAGNETIC FIELDS - ELECTROMAGNETIC SCATTERING - GALERKIN METHOD - HIGH RESOLUTION - MATHEMATICAL FILTERS
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- Internet Archive ID: DTIC_ADA586691
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50NUMERICAL ALGORITHMS FOR FINITE ELEMENT COMPUTATIONS
tecnologie segrete
“NUMERICAL ALGORITHMS FOR FINITE ELEMENT COMPUTATIONS” Metadata:
- Title: ➤ NUMERICAL ALGORITHMS FOR FINITE ELEMENT COMPUTATIONS
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- Internet Archive ID: ➤ numerical-algorithms-for-finite-element-computations
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Source: The Open Library
The Open Library Search Results
Available books for downloads and borrow from The Open Library
1Numerical algorithms
By E. V. Krishnamurthy

“Numerical algorithms” Metadata:
- Title: Numerical algorithms
- Author: E. V. Krishnamurthy
- Language: English
- Number of Pages: Median: 629
- Publisher: Affiliated East-West Press
- Publish Date: 1986
- Publish Location: New Delhi
“Numerical algorithms” Subjects and Themes:
- Subjects: Numerical analysis - Algorithms - Data processing
Edition Identifiers:
- The Open Library ID: OL24588210M
- Online Computer Library Center (OCLC) ID: 18474675
- All ISBNs: 9788185095141 - 8185095140
Access and General Info:
- First Year Published: 1986
- Is Full Text Available: Yes
- Is The Book Public: No
- Access Status: Borrowable
Online Access
Downloads Are Not Available:
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