Details

Subject(s)

• Approximation theory [Browse]

Publisher

• Society for Industrial and Applied Mathematics [Browse]

Library of Congress genre(s)

• Textbooks [Browse]

Series

Other titles in applied mathematics. [More in this series]

Summary note

This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the field's most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.

Bibliographic references

Includes bibliographical references (pages 329-355) and index.

System details

• Mode of access: World Wide Web.
• System requirements: Adobe Acrobat Reader.

Source of description

Description based on title page of print version.

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.

Show 24 more Contents items

Other format(s)

Also available in print version.

ISBN

1-61197-594-8

Publisher no.

OT164

LCCN

2019027108

OCLC

1119061092

Doi

• 10.1137/1.9781611975949

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