RT Journal Article
T1 Convergence and computation of simultaneous rational quadrature formulas
A1 Fidalgo Prieto, Ulises
A1 Illán, Jesús R.
A1 López Lagomasino, Guillermo
AB We discuss the convergence and numerical evaluation of simultaneous quadrature formulas which are exact for rational functions. The problem consists in integrating a single function with respect to different measures using a common set of quadrature nodes. Given a multi-index n, the nodes of the integration rule are the zeros of the multi-orthogonal Hermite–Padé polynomial with respect to (S, α, n), where S is a collection of measures, and α is a polynomial which modifies the measures in S. The theory is based on the connection between Gauss-type simultaneous quadrature formulas of rational type and multipoint Hermite–Padé approximation. The numerical treatment relies on the technique of modifying the integrand by means of a change of variable when it has real poles close to the integration interval. The output of some tests show the power of this approach in comparison with other ones in use.
PB Springer
SN 0029-599X (Print)
SN 0945-3245 (Online)
YR 2007
FD 2007-03
LK https://hdl.handle.net/10016/6278
UL https://hdl.handle.net/10016/6278
LA eng
NO 22 pages, no figures.-- MSC2000 codes: Primary 41A55. Secondary 41A28, 65D32.
NO MR#: MR2286008 (2008a:65049)
NO Zbl#: Zbl 1168.65326
NO The work of U.F.P. and G.L.L. was partially supported by Dirección General de EnseñanzaSuperior under grant BFM2003-06335-C03-02 and of G.L.L. by INTAS under Grant INTAS 03-51-6637. The work of J.R.I. was supported by a research grant from the Ministerio de Educación y Ciencia, project code MTM 2005-01320.
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RD 17 jun. 2024