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Computational Aspects of Orthogonal Polynomials

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Orthogonal Polynomials

Part of the book series: NATO ASI Series ((ASIC,volume 294))

Abstract

Our concern here is with computational methods for generating orthogonal polynomials and related quantities. We focus on the case where the underlying measure of integration is nonclassical. The main problem, then, is that of computing the coefficients in the basic recurrence relation satisfied by orthogonal polynomials. Two principal methods are considered, one based on modified moments, the other on inner product representations of the coefficients. The first method is the more economical one, but may be subject to ill-conditioning. A study is made of the underlying reasons for instability. The second method, suitably implemented, is more widely applicable, but less economical. A number of problem areas in the physical sciences and in applied mathematics are described where these methods find useful applications.

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Authors and Affiliations

  1. Department of Computer Science, Purdue University, West Lafayette, 47907, IN, USA

    Walter Gautschi

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  1. Walter Gautschi
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  1. Department of Mathematics, The Ohio State University, Columbus, Ohio, USA

    Paul Nevai

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© 1990 Kluwer Academic Publishers

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Gautschi, W. (1990). Computational Aspects of Orthogonal Polynomials. In: Nevai, P. (eds) Orthogonal Polynomials. NATO ASI Series, vol 294. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0501-6_9

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  • DOI: https://doi.org/10.1007/978-94-009-0501-6_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6711-9

  • Online ISBN: 978-94-009-0501-6

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