Orthogonal Polynomials - Computation and Approximation (Hardcover)

This is the first book on constructive methods for, and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of polynomials orthogonal on the real line (or a portion thereof), relative to a positive measure of integration. Topics which are particularly relevant to computation are emphasized. The second chapter develops computational methods for generating the coefficients in the basic three-term recurrence relation. The methods are of two kinds: moment-based methods and discretization methods. The former are provided with a detailed sensitivity analysis. Other topics addressed concern Cauchy integrals of orthogonal polynomials and their computation, a new discussion of modification algorithms, and the generation of Sobolev orthogonal polynomials. The final chapter deals with selected applications: the numerical evaluation of integrals, especially by Gauss-type quadrature methods, polynomial least squares approximation, moment-preserving spline approximation, and the summation of slowly convergent series. Detailed historic and bibliographic notes are appended to each chapter. The book will be of interest not only to mathematicians and numerical analysts, but also to a wide clientele of scientists and engineers who perceive a need for applying orthogonal polynomials.

General

Imprint:	Oxford UniversityPress
Country of origin:	United Kingdom
Series:	Numerical Mathematics and Scientific Computation
Release date:	April 2004
First published:	June 2004
Authors:	Walter Gautschi
Dimensions:	242 x 162 x 22mm (L x W x T)
Format:	Hardcover
Pages:	312
ISBN-13:	978-0-19-850672-0
Categories:	Books > Science & Mathematics > Mathematics > Numerical analysis Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematics for scientists & engineers Promotions
LSN:	0-19-850672-4
Barcode:	9780198506720

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