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Orthogonal polynomials: applications and computation

Published online by Cambridge University Press:  07 November 2008

Walter Gautschi
Walter Gautschi
Affiliation:
Department of Computer SciencesPurdue UniversityWest Lafayette, IN 47907–1398, USA E-mail: wxg@cs.purdue.edu
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We give examples of problem areas in interpolation, approximation, and quadrature, that call for orthogonal polynomials not of the classical kind. We then discuss numerical methods of computing the respective Gauss-type quadrature rules and orthogonal polynomials. The basic task is to compute the coefficients in the three-term recurrence relation for the orthogonal polynomials. This can be done by methods relying either on moment information or on discretization procedures. The effect on the recurrence coefficients of multiplying the weight function by a rational function is also discussed. Similar methods are applicable to computing Sobolev orthogonal polynomials, although their recurrence relations are more complicated. The paper concludes with a brief account of available software.

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Research Article
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Acta Numerica , Volume 5 , January 1996 , pp. 45 - 119
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Copyright © Cambridge University Press 1996

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