# Numerical Analysis: A Mathematical Introduction

Clarendon Press, 2002 - Mathematics - 496 pages
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.

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### 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