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Introduction to Numerical Analysis

  • J. Stoer
  • R. Bulirsch

Table of contents

  1. Front Matter
    Pages i-ix
  2. J. Stoer, R. Bulirsch
    Pages 1-36
  3. J. Stoer, R. Bulirsch
    Pages 37-116
  4. J. Stoer, R. Bulirsch
    Pages 117-158
  5. J. Stoer, R. Bulirsch
    Pages 159-243
  6. J. Stoer, R. Bulirsch
    Pages 244-313
  7. J. Stoer, R. Bulirsch
    Pages 314-403
  8. J. Stoer, R. Bulirsch
    Pages 404-535
  9. Back Matter
    Pages 597-609

About this book

Introduction

This book is based on a one-year introductory course on numerical analysis given by the authors at several universities in Germany and the United States. The authors concentrate on methods which can be worked out on a digital computer. For important topics, algorithmic descriptions (given more or less formally in ALGOL 60), as well as thorough but concise treatments of their theoretical founda­ tions, are provided. Where several methods for solving a problem are presented, comparisons of their applicability and limitations are offered. Each comparison is based on operation counts, theoretical properties such as convergence rates, and, more importantly, the intrinsic numerical properties that account for the reliability or unreliability of an algorithm. Within this context, the introductory chapter on error analysis plays a special role because it precisely describes basic concepts, such as the numerical stability of algorithms, that are indispensable in the thorough treatment of numerical questions. The remaining seven chapters are devoted to describing numerical methods in various contexts. In addition to covering standard topics, these chapters encom­ pass some special subjects not usually found in introductions to numerical analysis. Chapter 2, which discusses interpolation, gives an account of modem fast Fourier transform methods. In Chapter 3, extrapolation techniques for spe~d­ ing up the convergence of discretization methods in connection with Romberg integration are explained at length.

Keywords

Analysis Eigenvalue algorithms boundary element method calculus convergence differential equation integration interpolation mathematics minimum numerical analysis numerical method ordinary differential equation stability

Authors and affiliations

  • J. Stoer
    • 1
  • R. Bulirsch
    • 2
  1. 1.Institut für Angewandte MathematikUniversität Würzburg am HublandWürzburgFederal Republic of Germany
  2. 2.Institut für MathematikTechnische UniversitätMünchenFederal Republic of Germany

Bibliographic information