## Internality of generalized averaged Gauss rules and their truncations for Bernstein-Szegő weights

D. Lj. Djukić, L. Reichel, M. M. Spalević, and J. D. Tomanović

### Abstract

Generalized averaged Gauss quadrature formulas may have nodes outside the interval of integration. Quadrature rules with nodes outside the interval of integration cannot be applied to approximate integrals with an integrand that is defined on the interval of integration only. This paper investigates when generalized averaged Gauss quadrature rules for Bernstein-Szegő weight functions have all nodes in the interval of integration. Also truncated variants of these quadrature rules are considered. The relation between generalized averaged Gauss quadrature formulas and Gauss-Kronrod rules is explored.

Full Text (PDF) [316 KB], BibTeX

### Key words

Gauss quadrature, averaged Gauss quadrature, truncated generalized averaged Gauss quadrature, internality of quadrature rule

65D32, 65D30

### 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 [4] Vol. 13 (2002), pp. 119-147 Walter Gautschi: The interplay between classical analysis and (numerical) linear algebra - a tribute to Gene H. Golub [15] Vol. 45 (2016), pp. 371-404 Sotirios E. Notaris: Gauss-Kronrod quadrature formulae - A survey of fifty years of research

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