Approximation Theory and Approximation Practice

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.