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Orthogonal polynomials: Applications and computation. (English) Zbl 0871.65011
Iserles, A. (ed.), Acta Numerica Vol. 5, 1996. Cambridge: Cambridge University Press. 45-119 (1996).
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.

MSC:
 65D20 Computation of special functions, construction of tables 42C05 General theory of orthogonal functions and polynomials 65-02 Research monographs (numerical analysis) 65D05 Interpolation (numerical methods) 65Q05 Numerical methods for functional equations (MSC2000) 65D32 Quadrature and cubature formulas (numerical methods) 65B10 Summation of series (numerical analysis)