An Introduction to Numerical Analysis.pdf

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An Introduction to

Numerical Analysis

Endre Suli and David F. Mayers

University of Oxford

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

Cambridge University Press

The Edinburgh Building, Cambridge

, United Kingdom

Published in the United States of America by Cambridge University Press, New York

www.cambridge.org

Information on this title: www.cambridge.org/9780521810265

This book is in copyright. Subject to statutory exception and to the provision of

relevant collective licensing agreements, no reproduction of any part may take place

without the written permission of Cambridge University Press.

First published in print format

2003

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eBook (NetLibrary)

hardback

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hardback

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Cambridge University Press has no responsibility for the persistence or accuracy of

s for external or third-party internet websites referred to in this book, and does not

guarantee that any content on such websites is, or will remain, accurate or appropriate.

Contents

Preface

page vii

Solution of equations by iteration

1.1 Introduction

1.2 Simple iteration

1.3 Iterative solution of equations

1.4 Relaxation and Newton’s method

1.5 The secant method

1.6 The bisection method

1.7 Global behaviour

1.8 Notes

Exercises

Solution of systems of linear equations

2.1 Introduction

2.2 Gaussian elimination

2.3 LU factorisation

2.4 Pivoting

2.5 Solution of systems of equations

2.6 Computational work

2.7 Norms and condition numbers

2.8 Hilbert matrix

2.9 Least squares method

2.10 Notes

Exercises

Special matrices

3.1 Introduction

3.2 Symmetric positive deﬁnite matrices

3.3 Tridiagonal and band matrices

iii

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