Volume 9, pp. 39-52, 1999.

Quadrature formulas for rational functions

F. Cala Rodriguez, P. Gonzalez-Vera, and M. Jimenez Paiz

Abstract

Let $\omega$ be an $\mbox{L}_1$-integrable function on $[-1,1]$ and let us denote $$ I_{\omega}(f)=\int_{-1}^1 f(x)\omega(x)dx, $$ where $f$ is any bounded integrable function with respect to the weight function $\omega$. We consider rational interpolatory quadrature formulas (RIQFs) where all the poles are preassigned and the interpolation is carried out along a table of points contained in $\bar{\bf C}$. The main purpose of this paper is the study of the convergence of the RIQFs to $I_\omega(f)$.

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Key words

weight functions, interpolatory quadrature formulas, orthogonal polynomials, multipoint Padé–type approximants.

AMS subject classifications

41A21, 42C05, 30E10.

ETNA articles which cite this article

Vol. 16 (2003), pp. 143-164 J. Illán: A quadrature formula of rational type for integrands with one endpoint singularity