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Approximation theory and approximation practice

Author: Lloyd N Trefethen
Publisher: Philadelphia : Society for Industrial and Applied Mathematics, [2013]
Series: Other titles in applied mathematics.
Edition/Format:   Print book : EnglishView all editions and formats

An original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code.

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Document Type: Book
All Authors / Contributors: Lloyd N Trefethen
ISBN: 9781611972399 1611972396
OCLC Number: 806521965
Description: vii, 305 pages : illustrations (some color) ; 26 cm.
Contents: 1. Introduction --
2. Chebyshev Points and Interpolants --
3. Chebyshev Polynomials and Series --
4. Interpolants, Projections, and Aliasing --
5. Barycentric Interpolation Formula --
6. Weierstrass Approximation Theorem --
7. Convergence for Differentiable Functions --
8. Convergence for Analytic Functions --
9. Gibbs Phenomenon --
10. Best Approximation --
11. Hermite Integral Formula --
12. Potential Theory and Approximation --
13. Equispaced Points, Runge Phenomenon --
14. Discussion of High-Order Interpolation --
15. Lebesgue Constants --
16. Best and Near-Best --
17. Orthogonal Polynomials --
18. Polynomial Roots and Colleague Matrices --
19. Clenshaw-Curtis and Gauss Quadrature --20. Carathéodory-Fejér Approximation --
21. Spectral Methods --
22. Linear Approximation: Beyond Polynomials --
23. Nonlinear Approximation: Why Rational Functions --
24. Rational Best Approximation --
25. Two Famous Problems --
26. Rational Interpolation and Linearized Least-Squares --
27. Padé Approximation --
28. Analytic Continuation and Convergence Acceleration --
Appendix: Six Myths of Polynomial Interpolation and Quadrature --
References --
Series Title: Other titles in applied mathematics.
Responsibility: Lloyd N. Trefethen.
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