# Book:Walter Gautschi/Numerical Analysis: An Introduction

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## Walter Gautschi:

## Walter Gautschi: *Numerical Analysis: An Introduction*

Published $\text {1997}$, **BirkhĂ¤user**

- ISBN 978-08-176-3895-5

### Subject Matter

### Contents

**Preface**

**Chapter 0. Prologue**

**Chapter 1. Machine Arithmetic and Related Matters**- 1. Real Numbers, Machine Numbers, and Rounding
- 2. Machine Arithmetic
- 3. The Condition of a Problem
- 4. The Condition of an Algorithm
- 5. Computer Solution of a Problem; Overall Error
- Notes to Chapter 1
- Exercises and Machine Assignments to Chapter 1

**Chapter 2. Approximation and Interpolation**- 1. Least Squares Approximation
- 2. Polynomial Interpolation
- 3. Approximation and Interpolation by Spline Functions
- Notes to Chapter 2
- Exercises and Machine Assignments to Chapter 2

**Chapter 3. Numerical Differentiation and Integration**- 1. Numerical Differentiation
- 2. Numerical Integration
- Notes to Chapter 3
- Exercises and Machine Assignments to Chapter 3

**Chapter 4. Nonlinear Equations**- 1. Examples
- 2. Iteration, Convergence, and Efficiency
- 3. The Methods of Bisection and Sturm Sequences
- 4. Method of False Position
- 5. Secant Method
- 6. Newton's Method
- 7. Fixed Point Iteration
- 8. Algebraic Equations
- 9. Systems of Nonlinear Equations
- Notes to Chapter 4
- Exercises and Machine Assignments to Chapter 4

**Chapter 5. Initial Value Problems for ODEs - One-Step Methods**- 1. Local Description of One-Step Methods
- 2. Examples of One-Step Methods
- 3. Global Description of One-Step Methods
- 4. Error Monitoring and Step Control
- 5. Stiff Problems
- Notes to Chapter 5
- Exercises and Machine Assignments to Chapter 5

**Chapter 6. Initial Value Problems for ODEs - Multistep Methods**- 1. Local Description of Multistep Methods
- 2. Examples of Multistep Methods
- 3. Global Description of Multistep Methods
- 4. Analytic Theory of Order and Stability
- 5. Stiff Problems
- Notes to Chapter 6
- Exercises and Machine Assignments to Chapter 6

**Chapter 7. Two-Point Boundary Value Problems for ODEs**- 1. Existence and Uniqueness
- 2. Initial Value Techniques
- 3. Finite Difference Methods
- 4. Variational Methods
- Notes to Chapter 7
- Exercises and Machine Assignments to Chapter 7

**References**

**Subject Index**