Volume 41, pp. 1-12, 2014.

Estimating the error of Gauss-Turán quadrature formulas using their extensions

Aleksandar S. Cvetković and Miodrag M. Spalević

Abstract

We consider extensions of Kronrod-type and extensions obtained by generalized averaged Gaussian quadrature formulas for Gauss-Turán quadrature formulas. Existence and uniqueness of these extensions are considered. Their numerical construction is proposed. It is the first general method and is based on a combination of well-known numerical methods for Gauss-Turán, Gauss, Gauss-Kronrod, Anti-Gauss, and generalized averaged Gaussian quadratures. We employ these extensions for estimating the remainder terms in the Gauss-Turán quadratures. Numerical results are presented.

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Key words

quadrature rule, error estimate

AMS subject classifications

65D32, 65D30

ETNA articles which cite this article

Vol. 45 (2016), pp. 371-404 Sotirios E. Notaris: Gauss-Kronrod quadrature formulae - A survey of fifty years of research

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