Volume 9, pp. 65-76, 1999.

Orthogonal polynomials and quadrature

Walter Gautschi

Abstract

Various concepts of orthogonality on the real line are reviewed that arise in connection with quadrature rules. Orthogonality relative to a positive measure and Gauss-type quadrature rules are classical. More recent types of orthogonality include orthogonality relative to a sign-variable measure, which arises in connection with Gauss-Kronrod quadrature, and power (or implicit) orthogonality encountered in Turán-type quadratures. Relevant questions of numerical computation are also considered.

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Key words

orthogonal polynomials, Gauss-Lobatto, Gauss-Kronrod, and Gauss-Turán rules, computation of Gauss-type quadrature rules.

AMS subject classifications

33C45, 65D32, 65F15.

ETNA articles which cite this article

Vol. 9 (1999), pp. 26-38 G. S. Ammar, D. Calvetti, and L. Reichel: Computation of Gauss-Kronrod quadrature rules with non-positive weights
Vol. 45 (2016), pp. 371-404 Sotirios E. Notaris: Gauss-Kronrod quadrature formulae - A survey of fifty years of research

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