Orthogonal Polynomials

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ID: 296536
2004
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Abstract
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.
Reference Key
openalex_W1593505867 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Walter Gautschi
Journal Oxford University Press eBooks
Year 2004
DOI
10.1093/oso/9780198506720.001.0001
URL
https://doi.org/10.1093/oso/9780198506720.001.0001
Keywords Keywords not found

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