Book:Walter Gautschi/Numerical Analysis: An Introduction

Walter Gautschi: Numerical Analysis: An Introduction

Published $\text {1997}$, Birkhäuser

ISBN 978-08-176-3895-5

Subject Matter

• Numerical Analysis

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