Numerical Analysis: A Mathematical Introduction

Paperback | October 1, 2002

byMichelle Schatzman, John Taylor

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Numerical analysis explains why numerical computations work, or fail. This book is divided into four parts. Part I starts Part I starts with a guided tour of floating number systems and machine arithmetic. The exponential and the logarithm are constructed from scratch to present a new point ofview on questions well-known to the reader, and the needed knowledge of linear algebra is summarized. Part II starts with polynomial approximation (polynomial interpolation, mean-square approximation, splines). It then deals with Fourier series, providing the trigonometric version of least squareapproximations, and one of the most important numerical algorithms, the fast Fourier transform. Any scientific computation program spends most of its time solving linear systems or approximating the solution of linear systems, even when trying to solve non-linear systems. Part III is therefore aboutnumerical linear algebra, while Part IV treats a selection of non-linear or complex problems: resolution of linear equations and systems, ordinary differential equations, single step and multi-step schemes, and an introduction to partial differential equations. The book has been written having inmind the advanced undergraduate students in mathematics who are interested in the spice and spirit of numerical analysis. The book does not assume previous knowledge of numerical methods. It will also be useful to scientists and engineers wishing to learn what mathematics has to say about thereason why their numerical methods work - or fail.

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Numerical analysis explains why numerical computations work, or fail. This book is divided into four parts. Part I starts Part I starts with a guided tour of floating number systems and machine arithmetic. The exponential and the logarithm are constructed from scratch to present a new point ofview on questions well-known to the reader,...

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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Format:PaperbackDimensions:516 pages, 9.21 × 6.14 × 1.1 inPublished:October 1, 2002Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198508522

ISBN - 13:9780198508526

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Table of Contents

Part I: The entrance fee1. Floating numbers2. A flavour of numerical analysis3. Algebraic preliminariesPart II: Polynomial and trigonometric approximation of functions4. Interpolation and divided differences5. Least squares for polynomials6. Splines7. Fourier's world8. QuadraturePart III: Numerical linear algebra9. Gauss' world10. Theoretical interlude11. Iterations and recurrences12. Pythagoras' worldPart IV: Non-linear problems13. Spectra14. Non-linear equations and systems15. Solving differential systems16. Single step schemes17. Linear multi-step schemes18. Toward partial differential equationsBibliographyIndex

Editorial Reviews

"This exceptionally comprehensive and thorough book is what Schatzman ... has titled it--a mathematical introduction to numerical analysis. ... The text is clearly written and error free, and the mathematics is always rigorous. ... An excellent source for those 'interested in the spice and spirit of numerical analysis...'"--Choice