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Approximation theory and approximation practice Lloyd N. Trefethen (University of Oxford, Oxford, United Kingdom).

By: Trefethen, Lloyd N (Lloyd NicholasMaterial type: TextTextSeries: Society for Industrial and Applied Mathematics - OT 164Publisher: Philadelphia : SIAM, Society for Industrial and Applied Mathematics, [2020]Edition: ExtendedContent type: text Media type: computer Carrier type: online resourceISBN: 9781611975932 (HB)Subject(s): Approximation theoryAdditional physical formats: Print version:: Approximation theory and approximation practiceDDC classification: 41 TRE
Contents:
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 -- Carathéodory-Fejér approximation -- Spectral methods -- Linear approximation : beyond polynomials -- Nonlinear approximation : why rational functions? -- Rational best approximation -- Two famous problems -- Rational interpolation and linearized least-squares -- Padé approximation -- Analytic continuation and convergence acceleration.
Summary: "Including two new appendices, this extended edition of Trefethen's textbook covers classical polynomial and rational approximation theory for the twenty-first century"-- Provided by publisher.
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Item type Current library Shelving location Call number Materials specified Status Date due Barcode
Books TIFR CAM Library
SERIES 41 TRE (Browse shelf(Opens below)) Checked out to Praveen C (PCA052) 02/08/2024 M12167

Includes bibliographical references and index.

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 -- Carathéodory-Fejér approximation -- Spectral methods -- Linear approximation : beyond polynomials -- Nonlinear approximation : why rational functions? -- Rational best approximation -- Two famous problems -- Rational interpolation and linearized least-squares -- Padé approximation -- Analytic continuation and convergence acceleration.

"Including two new appendices, this extended edition of Trefethen's textbook covers classical polynomial and rational approximation theory for the twenty-first century"-- Provided by publisher.

Description based on print version record and CIP data provided by publisher.

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