Orthogonal polynomials are a widely used class of mathematical functions that are helpful in the solution of many important technical problems. This book provides a systematic development of computational techniques, including a suite of computer programs in Matlab downloadable from the Internet, to generate orthogonal polynomials. Series: Numerical Mathematics & Scientific Computation. Num Pages: 312 pages, 9 b/w line drawings. BIC Classification: PBKS; PBW; PDE; TBJ. Category: (P) Professional & Vocational. Dimension: 243 x 174 x 29. Weight in Grams: 608. . 2004. Illustrated. hardcover. . . . . Books ship from the US and Ireland.

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Bibliographic Details

Title: Orthogonal Polynomials: Computation and Approximation (Numerical Mathematics and Scientific Computation)
Publisher: OUP Oxford
Publication Date: 2004
Language: English
ISBN 10: 0198506724
ISBN 13: 9780198506720
Binding: Hardcover
Condition: New

About this title

Synopsis

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.

About the Author

Walter Gautshi is Professor Emeritus at Purdue University, USA.

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