Approximation Theory and Approximation PracticeThis textbook, with 163 figures and 210 exercises, was published in 2013. It is available from SIAM and from Amazon.Unusual features:
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- 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 Orthogonal polynomials
- chap18.m Polynomial roots and colleague matrices
- chap19.m Clenshaw-Curtis and Gauss quadrature
- chap20.m Carathéodory-Fejér 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 linearized least-squares
- chap27.m Padé approximation
- chap28.m Analytic continuation and convergence acceleration
- refs.m References
p 22: Exercise 3.6: the exponent k-1 should be (k-1)/2.
p 26: subscripts m should be n; -k(mod 2n) should be (-k)(mod 2n)
p 82: Cauchy stated a related formula but not exactly "the same result"
pp 147, 151: Eqs. (19.10) and (19.12) are incorrectly copied from
Trefethen (2008): (n-2\nu-1)^{2\nu+1} should be (2n+1-\nu)^\nu
p 166: Eq. (21.2) is incorrect (p. 166 and inside back cover).
p 229: the summation at the bottom needs a square root
p 256: Lottka should be Lotka
p 304: Richardson extrapolation should list pages 257-258