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Zbl 0871.65011
Gautschi, Walter
Orthogonal polynomials: Applications and computation. (English)
[A] Iserles, A. (ed.), Acta Numerica Vol. 5, 1996. Cambridge: Cambridge University Press. 45-119 (1996). ISBN 0-521-57234-7/hbk

This is an extended survey paper on recent work on orthogonal polynomials and their application in interpolation, approximation and quadrature. It contains many details and excellent references to recent (and older) literature and information on available software. Among the subjects treated are a motivational introduction based on Gauss-type quadrature rules, computation of the coefficients in the three-term recurrence relation, rational interpolation, constrained least squares approximation, slowly convergent infinite series, moment-based methods, and Sobolev orthogonal polynomials (if derivatives are also to be approximated). The paper is a reference not to be missed by anyone seriously interested in the subject.
[W.Govaerts (Gent)]

MSC 2000:: *65D20 Computation of special functions
42C05 General theory of orthogonal functions and polynomials
65-02 Research monographs (numerical analysis)
65D05 Interpolation (numerical methods)
65Q05 Numerical methods for functional equations
65D32 Quadrature formulas (numerical methods)
65B10 Summation of series

Keywords: research survey; interpolation; Gauss-type quadrature; recurrence relation; rational interpolation; least squares approximation; slowly convergent infinite series; moment-based methods; Sobolev orthogonal polynomials

Cited in: Zbl 1225.65005 Zbl 1090.42015 Zbl 1067.65024

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