Trefethen, Lloyd N creator Trefethen, Lloyd N text Philadelphia : Society for Industrial and Applied Mathematics 2013 monographic eng

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vii, 305 pages : illustrations (some color) ; 26 cm. 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. 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. / Lloyd N Trefethen Mathematics General principles of mathematics Approximation theory Polynomials 511.4 TRE 9789386235442 :Raghav Books Private Limited :A-184 Nand Gram Ghaziabad 211201 20211206162037.0