Introduction to Numerical Analysis

1. Front Matter

   Pages i-ix

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2. Error Analysis

   • J. Stoer, R. Bulirsch

   Pages 1-36

3. Interpolation

   • J. Stoer, R. Bulirsch

   Pages 37-116

4. Topics in Integration

   • J. Stoer, R. Bulirsch

   Pages 117-158

5. Systems of Linear Equations

   • J. Stoer, R. Bulirsch

   Pages 159-243

6. Finding Zeros and Minimum Points by Iterative Methods

   • J. Stoer, R. Bulirsch

   Pages 244-313

7. Eigenvalue Problems

   • J. Stoer, R. Bulirsch

   Pages 314-403

8. Ordinary Differential Equations

   • J. Stoer, R. Bulirsch

   Pages 404-535

9. Iterative Methods for the Solution of Large Systems of Linear Equations. Some Further Methods

   • J. Stoer, R. Bulirsch

   Pages 536-596

10. Back Matter

    Pages 597-609

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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.

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

• Institut für Angewandte Mathematik, Universität Würzburg am Hubland, Würzburg, Federal Republic of Germany

  J. Stoer

• Institut für Mathematik, Technische Universität, München, Federal Republic of Germany

  R. Bulirsch

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