Self-Validating Numerics for Function Space Problems : Computation with Guarantees for Differential and Integral Equations

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Self-Validating Numerics for Function Space Problems. Abstract: Self-Validating Numerics for Function Space Problems Content: Front Cover Self-Validating Numerics for Function Space Problems Copyright Page Dedication Table of Contents Preface Acknowledgments Chapter1. Introduction E-Methods Ultra-arithmetic Computer Arithmetic Suggestions to the Reader Chapter 2. Mathematical Preliminaries 2.1 Basic Formulation of Self-Validating Methods in M 2.2 A Broader Setting for Self-Validating Methods Chapter 3. Ultra-arithmetic and Roundings 3.1 Spaces, Bases, Roundings, and Approximate Operations 3.2 Spaces, Bases, and Roundings for Validation Chapter 4. Methods for Functional Equations. 4.1 Methods for Linear Equations4.2 Methods for Nonlinear Function Equations Chapter 5. Iterative Residual Correction 5.1 Arithmetic Implications of IRC 5.2 IRC for Initial-Value Problems and Volterra Integral Equations 5.3 Iterative Residual Correction with Carry 5.4 A Formalism for IRC in Function Space Chapter 6. Comments on Programming Language Chapter 7. Application and Illustrative Computation 7.1 Review of the Computational Process 7.2 Illustrative Computation Glossaries References.