Approximation Theory and Approximation Practice (Applied Mathematics)

Synopsis

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, University Of Oxford. Includes Bibliographical References And Index.