Volume 61, pp. 92-104, 2024.

Error estimates for Gauss-type quadrature rules for variable-sign weight functions

Jelena Tomanović

Abstract

When Gauss quadrature rules are applied, the weight function is usually assumed to be nonnegative on the interval of integration. This paper considers recently introduced Gauss-type quadrature formulas with respect to weight functions that change sign in the interior of the interval of integration. To economically estimate the error of these formulas, we propose extensions based on Gauss-Kronrod, averaged Gauss, and generalized averaged Gauss quadrature rules. Numerical examples illustrate the accuracy of the introduced error estimates.

Full Text (PDF) [296 KB], BibTeX

Key words

Gauss quadrature formula, variable-sign weight function, error estimate

AMS subject classifications

65D30, 65D32, 41A55

Links to the cited ETNA articles

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

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