Conjugate Gradient Type Methods for Ill-Posed Problems - Info and Reading Options
By Martin Hanke
"Conjugate Gradient Type Methods for Ill-Posed Problems" was published by Taylor & Francis Group in 2017 - London, it has 144 pages and the language of the book is English.
“Conjugate Gradient Type Methods for Ill-Posed Problems” Metadata:
- Title: ➤ Conjugate Gradient Type Methods for Ill-Posed Problems
- Author: Martin Hanke
- Language: English
- Number of Pages: 144
- Publisher: Taylor & Francis Group
- Publish Date: 2017
- Publish Location: London
“Conjugate Gradient Type Methods for Ill-Posed Problems” Subjects and Themes:
- Subjects: ➤ Conjugate gradient methods - Improperly posed problems - Numerical analysis - Méthode du gradient conjugué - Analyse numérique - Problèmes mal posés
Edition Identifiers:
- The Open Library ID: OL33777133M - OL3747255W
- ISBN-13: 9781351458337
- All ISBNs: 9781351458337
AI-generated Review of “Conjugate Gradient Type Methods for Ill-Posed Problems”:
"Conjugate Gradient Type Methods for Ill-Posed Problems" Description:
Open Data:
Cover -- Half title -- Title Page -- Copyright Page -- Table of Contents -- 1 Preface -- Notation -- 2 Conjugate Gradient Type Methods -- 2.1 Krylov subspace methods -- 2.2 Two particular conjugate gradient type methods -- - The minimal residual method (MR) -- - The conjugate gradient method (CG) -- 2.3 Conjugate gradient type methods using TT* -- - CG applied to the normal equation (CGNE) -- -The minimal error method (CGME) -- 2.4 Basic relations between conjugate gradient type methods -- 2.5 Implementing both MR and CG in one scheme -- 2.6 Stability issues -- Notes and remarks -- 3 Regularizing Properties of MR and CGNE -- 3.1 Monotonicity, convergence and divergence -- 3.2 Convergence rate estimates -- 3.3 The discrepancy principle -- 3.4 A heuristic stopping rule -- Notes and remarks -- 4 Regularizing Properties of CG and CGME -- 4.1 Monotonicity, convergence and divergence -- 4.2 Failure of the discrepancy principle: a counterexample -- 4.3 An order-optimal stopping rule -- 4.4 A heuristic stopping rule -- Notes and remarks -- 5 On the Number of Iterations -- 5.1 General estimates for the stopping index -- 5.2 The counterexample revisited -- 5.3 An application: image reconstruction -- Notes and remarks . -- 6 A Minimal Residual Method for Indefinite Problems -- 6.1 MR-11, a variant of MR -- 6.2 On the zeros of the residual polynomials -- 6.3 Convergence and divergence -- 6.4 Stopping rules for MR-11 -- 6.5 Estimates for the stopping index -- 6.6 The image reconstruction problem -- 6.7 The sideways heat equation -- Notes and remarks -- References -- Index
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