Some remarks on the construction of extended Gaussian quadrature rules

Monegato, Giovanni

doi:10.1090/S0025-5718-1978-0458810-7

Some remarks on the construction of extended Gaussian quadrature rules
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by Giovanni Monegato PDF

Math. Comp. 32 (1978), 247-252 Request permission

Abstract:

We recall some results from a paper by Szegö on a class of polynomials which are related to extended Gaussian quadrature rules. We show that a very efficient algorithm, for the computation of the abscissas of the rules in question, was already described in that paper. We also point out that this method extends to rules for integrals with an ultraspherical-type weight function. A bound for the error of some of the above rules is also given.

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Orthogonal Polynomials