/ Lloyd N. Trefethen (University of Oxford, Oxford, United Kingdom).
EDITION STATEMENT
Edition Statement
Extended Edition.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Philadelphia :
Name of Publisher, Distributor, etc.
SIAM, Society for Industrial and Applied Mathematics,
Date of Publication, Distribution, etc.
2020.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references and index.
CONTENTS NOTE
Text of Note
Chebyshev points and interpolants -- Chebyshev polynomials and series -- Interpolants, projections, and aliasing -- Barycentric interpolation formula -- Weierstrass approximation theorem -- Convergence for differentiable functions -- Convergence for analytic functions -- Gibbs phenomenon -- Best approximation -- Hermite integral formula -- Potential theory and approximation -- Equispaced points, runge phenomenon -- Discussion of high-order interpolation -- Lebesgue constants -- Best and near-best -- Orthogonal polynomials -- Polynomial roots and colleague matrices -- Clenshaw-Curtis and Gauss quadrature -- Carath�eodory-Fej�er approximation -- Spectral methods -- Linear approximation : beyond polynomials -- Nonlinear approximation : why rational functions? -- Rational best approximation -- Two famous problems -- Rational interpolation and linearized least-squares -- Pad�e approximation -- Analytic continuation and convergence acceleration.
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SUMMARY OR ABSTRACT
Text of Note
"Including two new appendices, this extended edition of Trefethen's textbook covers classical polynomial and rational approximation theory for the twenty-first century"--