Orthogonal polynomials : computation and approximation /
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| Author / Creator: | Gautschi, Walter, 1927- author. |
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| Imprint: | Oxford ; New York : Oxford University Press, 2004. |
| Description: | 1 online resource (viii, 301 pages) : illustrations. |
| Language: | English |
| Series: | Numerical mathematics and scientific computation Oxford science publications Numerical mathematics and scientific computation. Oxford science publications. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11143617 |
| Summary: | 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.<br> |
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| Physical Description: | 1 online resource (viii, 301 pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages 261-282) and index. |
| ISBN: | 1423771087 9781423771081 9786610758869 6610758867 9780198506720 0198506724 1280758864 9781280758867 0191545058 9780191545054 |