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 ${\text{L}}_1$-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 $\overline{\mathbf{C}}$. 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