Introduction to Numerical Analysis

1. Front Matter

   Pages i-xiii

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2. Error Analysis

   • J. Stoer, R. Bulirsch

   Pages 1-36

3. Interpolation

   • J. Stoer, R. Bulirsch

   Pages 37-124

4. Topics in Integration

   • J. Stoer, R. Bulirsch

   Pages 125-166

5. Systems of Linear Equations

   • J. Stoer, R. Bulirsch

   Pages 167-259

6. Finding Zeros and Minimum Points by Iterative Methods

   • J. Stoer, R. Bulirsch

   Pages 260-329

7. Eigenvalue Problems

   • J. Stoer, R. Bulirsch

   Pages 330-427

8. Ordinary Differential Equations

   • J. Stoer, R. Bulirsch

   Pages 428-569

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

   • J. Stoer, R. Bulirsch

   Pages 570-645

10. Back Matter

    Pages 646-660

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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.

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

• Institut für Angewandte Mathematik, Universität Würzburg, Würzburg, Germany

  J. Stoer

• Institut für Mathematik, Technische Universität, München, Germany

  R. Bulirsch

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