TY  - BOOK
AU  - Trefethen,Lloyd N.
TI  - Approximation theory and approximation practice
SN  - 9781611972399 (alk. paper)
U1  - 511.4 23
PY  - 2013///
CY  - Philadelphia
PB  - SIAM
KW  - Approximation theory
N1  - Includes bibliographical references (pages 273-298) and index; 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 --
Index
N2  - An original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code
ER  -