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