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Approximation theory and approximation practice / Lloyd N. Trefethen.

By: Material type: TextTextPublication details: Philadelphia : SIAM, c2013.Description: vii, 305 p. : illustrations (some color) ; 26 cmISBN:
  • 9781611972399 (alk. paper)
Subject(s): DDC classification:
  • 511.4 23 T786
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 -- Index.
Summary: An original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 511.4 T786 (Browse shelf(Opens below)) Available 135426
Total holds: 0

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.

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

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