Scientific Computing, Computer Arithmetic, and Validated Numerics - Info and Reading Options

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Intro -- In Memory of Walter Krämer -- Preface -- Organization -- Contents -- Interval Arithmetic and Interval Functions -- Hausdorff Continuous Interval Functions and Approximations -- 1 Introduction -- 2 Classes of Interval Functions: Basic Results -- 2.1 Basic Notation and Definitions: Baire Continuous Functions -- 2.2 Arithmetic Operations in H(R) -- 2.3 The Set of H-Continuous Functions as a Linear Space -- 3 Hausdorff Approximations Using Step Functions -- 3.1 Hausdorff Distance and Modulus of H-Continuity -- 3.2 Interval Step Functions as an Approximation Tool -- 4 Approximation by Sigmoid Functions -- 4.1 Approximation by Sigmoid Logistic Functions -- 4.2 Estimate for the H-Distance in Terms of the Rate Parameter -- 5 Conclusions -- References -- Replacing Branches by Polynomials in Vectorizable Elementary Functions -- 1 Introduction -- 2 Mathematical Functions Implementation Workflow -- 3 Polynomial-Based Reconstruction Technique -- 3.1 How to Compute Polynomial Mapping -- 3.2 Conditions for the Polynomial -- 3.3 The Choice of the Interpolation Points -- 3.4 Towards a Priori Conditions -- 3.5 Algorithm -- 4 Conclusion -- References -- The Forthcoming IEEE Standard 1788 for Interval Arithmetic -- 1 What Intervals Are and Do -- 1.1 Basic Ideas -- 1.2 Definition of Interval Operations -- 2 Why Do Intervals Need New Algorithms? -- 2.1 Example: Interval Version of Newton's Iteration -- 2.2 Lessons from the Example -- 3 Genesis of the Interval Standard Project -- 3.1 The Need -- 3.2 Setting up a Working Group -- 4 1788 Interval Principles -- 4.1 Definition of an Interval -- 4.2 The Levels Structure -- 5 Exception Handling -- 5.1 A Hypothetical Scenario -- 5.2 Theoretical Context -- 5.3 Decorations -- 6 Difficulties the Group Encountered -- 7 Current State -- A Proof of Interval Newton Properties -- References -- Uncertainty

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