Introduction to Numerical Analysis

  • J. Stoer
  • R. Bulirsch

Part of the Texts in Applied Mathematics book series (TAM, volume 12)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. J. Stoer, R. Bulirsch
    Pages 1-36
  3. J. Stoer, R. Bulirsch
    Pages 37-124
  4. J. Stoer, R. Bulirsch
    Pages 125-166
  5. J. Stoer, R. Bulirsch
    Pages 167-259
  6. J. Stoer, R. Bulirsch
    Pages 260-329
  7. J. Stoer, R. Bulirsch
    Pages 330-427
  8. J. Stoer, R. Bulirsch
    Pages 428-569
  9. Back Matter
    Pages 646-660

About this book

Introduction

On the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for handling sparse matrices. We will explain some of these techniques in connection with the Cholesky algorithm for solving positive definite linear systems. The chapter on eigenvalue problems was enlarged by a section on the Lanczos algorithm; the sections on the LR and QR algorithm were rewritten and now contain a description of implicit shift techniques. In order to some extent take into account the progress in the area of ordinary differential equations, a new section on implicit differential equa­ tions and differential-algebraic systems was added, and the section on stiff differential equations was updated by describing further methods to solve such equations.

Keywords

Eigenvalue Mathematica algebra calculus differential equation integration interpolation minimum numerical analysis numerical method ordinary differential equation

Authors and affiliations

  • J. Stoer
    • 1
  • R. Bulirsch
    • 2
  1. 1.Institut für Angewandte MathematikUniversität WürzburgWürzburgGermany
  2. 2.Institut für MathematikTechnische UniversitätMünchenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2272-7
  • Copyright Information Springer-Verlag New York 1993
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-2274-1
  • Online ISBN 978-1-4757-2272-7
  • Series Print ISSN 0939-2475
  • About this book
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