Volume 9, pp. 39-52, 1999.

Quadrature formulas for rational functions

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

Abstract

Let ω be an L1-integrable function on [1,1] and let us denote Iω(f)=11f(x)ω(x)dx, where f is any bounded integrable function with respect to the weight function ω. 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 C¯. The main purpose of this paper is the study of the convergence of the RIQFs to Iω(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