Mathematics of approximation

by De Villiers, Johan

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Title Statements

Full title :Mathematics of approximation / Johan de Villiers.

Summary

The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in the general setting of normed linear spaces and inner product spaces; best uniform polynomial approximation; orthogonal polynomials; Newton-Cotes , Gauss and Clenshaw-Curtis quadrature; the Euler-Maclaurin formula ; approximation of periodic functions; the uniform convergence of Fourier series; spline approximation,with an extensive treatment of local spline interpolation,and its application in quadrature. Exercises are provided at the end of each chapter.

Edition Statements

Publication Date:cop. 2012.

Publication Statements

Publisher(s):Atlantis Press
Place of Publication:Amsterdam
Language:eng
Publication Date:cop. 2012.

Notes

Includes index.

The Physical Object

Description:1 online resource.

Edition Identifiers

ISBN:9789491216503, 9491216503
DOI:10.2991/978-94-91216-50-3
oclc:ocn905285712
Dewey Decimal:511/.4

Polynomial Interpolation Formulas -- Error Analysis for Polynomial Interpolation -- Polynomial Uniform Convergence -- Best Approximation -- Approximation Operators -- Best Uniform Polynomial Approximation -- Orthogonality -- Interpolatory Quadrature -- Approximation of Periodic Functions -- Spline Approximation.