Numerical Method

The development and analysis of constructive algorithms in Numerical Mathematics has become a focus of applied mathematics since the practical realization of these algorithms by electronic computers is no longer restricted to trivial examples. This book describes algorithmic solutions whose basic id...

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Bibliographic Details
Main Author: Wolfgang Boehm
Other Authors: Hartmut Prautzsch
Format: Printed Book
Published: Hyderabad Universities Press 2003
Subjects:
Numerical analysis.
Table of Contents:
  • I. Fundamental Concepts
  • 1. Algorithms and Error Propagation
  • 2. Matrices
  • II. Linear Equations and Inequalities
  • 3. Gaussian Elimination
  • 4. The LU Factorization
  • 5. The Exchange Algorithm
  • 6. The Cholesky Factorization
  • 7. The QU Factorization
  • 8. Relaxation Methods
  • 9. Data Fitting
  • 10. Linear Optimization
  • III. Iteration
  • 11. Vector Iteration
  • 12. The LR Algorithm
  • 13. One-Dimensional Iteration
  • 14. Multi-Dimensional Iteration
  • 15. Roots of Polynomials
  • 16. Bernoulli's Method
  • 17. The QD Algorithm
  • IV. Interpolation and Discrete Approximation
  • 18. Interpolation
  • 19. Discrete Approximation
  • 20. Polynomials in Bezier Form
  • 21. Splines
  • V. Numerical Differentiation and Integration
  • 22. Numerical Differentiation and Integration
  • 23. Extrapolation
  • 24. One-Step Methods for Differential Equations
  • 25. Linear Multi-Step Methods for Differential Equations
  • 26. The Methods by Ritz and Galerkin
  • 27. The Finite Element Method
  • 28. Bibliography.

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