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Approximation Theory and Approximation Practice / Lloyd N Trefethen

By: Contributor(s): Material type: TextTextPublisher number: :Raghav Books Private Limited | :A-184 Nand Gram Ghaziabad Publication details: Philadelphia : Society for Industrial and Applied Mathematics, 2013Description: vii, 305 pages : illustrations (some color) ; 26 cmISBN:
  • 9789386235442
Subject(s): DDC classification:
  • 511.4 TRE
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: Approximation Theory and Approximation Practice is a textbook on classical polynomial and rational approximation theory for the twenty-first century. It is aimed at advanced undergraduates and graduate students across all of applied mathematics. --Back cover.
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Holdings
Item type Current library Call number Status Notes Barcode
Mathematics Departmental Library Mathematics Departmental Library SNU LIBRARY 511.4 TRE (Browse shelf(Opens below)) Available NBHM M418
Books Books SNU LIBRARY 511.4 TRE (Browse shelf(Opens below)) Not For Loan 28142
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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.

Approximation Theory and Approximation Practice is a textbook on classical polynomial and rational approximation theory for the twenty-first century. It is aimed at advanced undergraduates and graduate students across all of applied mathematics. --Back cover.

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