Quadratures associated with pseudo-orthogonal rational functions on the real half line with poles in [-∞, 0]

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:237

Article

Bultheel, Adhemar¹  Gonzalez-Vera, Pablo²  Njastad, Olav³ 

[1] Katholieke Univ Leuven, Dept Comp Sc, B-3001 Heverlee, Belgium

[2] Univ La Laguna, Dept Math Anal, Tenerife, Spain

[3] Norwegian Univ Sci & Technol, Dept Math Sci, N-7034 Trondheim, Norway

关键词: Numerical quadrature;    Quasi;    and pseudo-orthogonal rational functions;   

DOI  :  10.1016/j.cam.2012.06.037

来源: Elsevier

【 摘 要 】

We consider a positive measure on [0, infinity) and a sequence of nested spaces L-0 subset of L-1 subset of L-2 ... Of rational functions with prescribed poles in [-infinity, 0]. Let {phi(k)}(k=0)(infinity), with phi(0) is an element of L-0 and phi(k) is an element of L-k \ Lk-1, k = 1, 2, ... be the associated sequence of orthogonal rational functions. The zeros of phi(n) can be used as the nodes of a rational Gauss quadrature formula that is exact for all functions in L-n . Ln-1, a space of dimension 2n. Quasi- and pseudo-orthogonal functions are functions in L-n that are orthogonal to some subspace of Ln-1. Both of them are generated from phi(n) and phi(n-1) and depend on a real parameter tau. Their zeros can be used as the nodes of a rational Gauss-Radau quadrature formula where one node is fixed in advance and the others are chosen to maximize the subspace of L-n . Ln-1 where the quadrature is exact. The parameter tau is used to fix a node at a preassigned point. The space where the quadratures are exact has dimension 2n - 1 in both cases but it is in Ln-1 . Z(n-1) in the quasi-orthogonal case and it is in L-n .Ln-2 in the pseudo-orthogonal case. (c) 2012 Elsevier B.V. All rights reserved.

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