Validated Numerics by Tucker, Warwick -- Read -- Imperial Library of Trantor

Index

Cover Title Copyright Contents preface Introduction

What Is Validated Numerics? The Scope and Aim of This Book Further Reading Acknowledgments

Chapter 1. Computer Arithmetic

1.1 Positional Systems 1.2 Floating Point Numbers 1.3 Rounding 1.4 Floating Point Arithmetic 1.5 The IEEE Standard 1.6 Examples of Floating Point Computations 1.7 Computer Lab I

Chapter 2. Interval Arithmetic

2.1 Real Intervals 2.2 Real Interval Arithmetic 2.3 Extended Interval Arithmetic 2.4 Floating Point Interval Arithmetic

Chapter 3. Interval Analysis

3.1 Interval Functions 3.2 Centered Forms 3.3 Monotonicity 3.4 Computer Lab II

Chapter 4. Automatic Differentiation

4.1 First-Order Derivatives 4.2 Higher-Order Derivatives 4.3 Higher-Order Enclosures 4.4 Computer Lab III

Chapter 5. Interval Analysis in Action

5.1 Zero-Finding Methods 5.2 Optimization 5.3 Quadrature 5.4 Computer Lab IV

Chapter 6. Ordinary Differential Equations

6.1 A Gentle Mathematical Introduction 6.2 Simple Enclosure Methods 6.3 High-Order Methods 6.4 Rigorous High-Order Examples

Appendix A. Mathematical Foundations

A.1 The Rational Numbers A.2 What Is a Real Number? A.3 Completeness A.4 Fixed-Point Theorems

Appendix B. Program Codes

B.1 IEEE Constants B.2 Changing Rounding Modes B.3 A Sample Code in C++

Bibliography Index

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