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Convergence and computation of simultaneous rational quadrature formulas

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URI: https://hdl.handle.net/10016/6278
ISSN: 0029-599X (Print)
ISSN: 0945-3245 (Online)
DOI: 10.1007/s00211-006-0056-8
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convergence_lagomasino_nm_2007_ps.pdf (274.15 KB)
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2007-03
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Springer
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Abstract
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.
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22 pages, no figures.-- MSC2000 codes: Primary 41A55. Secondary 41A28, 65D32.
MR#: MR2286008 (2008a:65049)
Zbl#: Zbl 1168.65326
Keywords
Simultaneous integration rule, Gauss-like rational quadrature formula, Meromorphic integrand
Bibliographic citation
Numerische Mathematik, 2007, vol. 106, n. 1, p. 99-128
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