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Computational Aspects of Orthogonal Polynomials

  • Walter Gautschi
Part of the NATO ASI Series book 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.

Keywords

Orthogonal Polynomial Recurrence Relation Chebyshev Polynomial Quadrature Rule Gaussian Quadrature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Walter Gautschi
    • 1
  1. 1.Department of Computer SciencePurdue UniversityWest LafayetteUSA

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