Numerical Analysis: A Mathematical Introduction

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Clarendon Press, 2002 - Mathematics - 496 pages
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This book provides professionals and students with a thorough understanding of the interface between mathematics and scientific computation. Ranging from classical questions to modern techniques, it explains why numerical computations succeed or fail. The book is divided into four sections, with an emphasis on the use of mathematics as a tool in determining the success rate of numerical methods. The text requires only a modest level of mathematical training, and is ideally suited for scientists and students in mathematics, physics and engineering.
 

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Contents

The entrance fee
1
A flavour of numerical analysis
11
Algebraic preliminaries
25
Polynomial and trigonometric approximation
47
Leastsquares approximation for polynomials
77
Splines
106
Fouriers world
133
Quadrature
165
Pythagoras world
290
Nonlinear problems
305
Nonlinear equations and systems
331
Solving differential systems
362
Singlestep schemes
385
Linear multistep schemes
414
Towards partial differential equations
439
References
479

Numerical linear algebra
205
Theoretical interlude
240
Iterations and recurrence
257

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About the author (2002)

Professor Michelle Schatzman, MAPLY, 21 Avenue Claude Bernard, UCBL, F-69622 Villeurbanne Cedex, Tel: +33 4 72 44 85 26, Fax: +33 4 74 22 80 53, Email: schatz@maply.univ-lyon1.fr

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