Approximation Theory and Approximation PracticeThis is a partially completed draft of the textbook "Approximation Theory and Approximation Practice" © 2011 Lloyd N. Trefethen, to be published in 2012 or 2013.Readers are welcome to take a look at this, and in exchange are requested to send suggestions and corrections to Prof. Trefethen at trefethen@maths.ox.ac.uk. |
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The book
M-files
- ATAPJune11files.tar.gz : All the M-files
- chap1.m : Introduction
- chap2.m : Chebyshev points and interpolants
- chap3.m : Chebyshev polynomials and series
- chap4.m : Interpolants, truncations, and aliasing
- chap5.m : Barycentric interpolation formula
- chap6.m : Weierstrass approximation theorem
- chap7.m : Convergence for differentiable functions
- chap8.m : Convergence for analytic functions
- chap9.m : Gibbs phenomenon
- chap10.m : Best approximation
- chap11.m : Hermite integral formula
- chap12.m : Potential theory and approximation
- chap13.m : Equispaced points, Runge phenomenon
- chap14.m : Discussion of higher-order polynomial interpolation.
- chap15.m : Lebesgue constants
- chap16.m : Best and near-best
- chap17.m : Legendre and other orthogonal polynomials
- chap18.m : Polynomial roots and colleague matrices
- chap19.m : Clenshaw-Curtis and Gauss quadrature
- chap20.m : Caratheodory-Fejer approximation
- chap21.m : Spectral methods
- chap22.m : Linear approximations: beyond polynomials
- chap23.m : Nonlinear approximations: why rational functions?
- chap24.m : Rational best approximation
- chap25.m : Two famous problems
- chap26.m : Rational interpolation and least-squares
- refs.m : References