Numerical Analysis: A Mathematical Introduction

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.

"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

CONTENTS

I: The entrance fee
1. Floating numbers
2.  A flavour of numerical analysis
3. Algebraic preliminaries
II: Polynomial and trigonometric approximation
4. Interpolation and divided differences
5. Least-squares approximation for polynomials
6. Splines
7. Fourier's world
8. Quadrature
III: Numerical linear algebra
9. Gauss's world
10. Theoretical interlude
11. Iterations and recurrence
12. Pythagoras' world
IV: Nonlinear problems
13. Spectra
14. Nonlinear equations and systems
15. Solving differential systems
16. Single-step schemes
17. Linear multistep schemes
18. Toward partial differential equations
References
Index