A matricial computation of rational quadrature formulas on the unit circle

被引：0
作者：
Adhemar Bultheel
Maria-José Cantero
机构：
[1] K.U. Leuven,Department of Computer Science
[2] University of Zaragoza,Department of Applied Mathematics
来源：
Numerical Algorithms | 2009年 / 52卷
关键词：
Orthogonal rational functions; Para-orthogonal rational functions; Szegő quadrature formulas; Möbius transformations; 42C05;
D O I：
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学科分类号：
摘要：
A matricial computation of quadrature formulas for orthogonal rational functions on the unit circle, is presented in this paper. The nodes of these quadrature formulas are the zeros of the para-orthogonal rational functions with poles in the exterior of the unit circle and the weights are given by the corresponding Christoffel numbers. We show how these nodes can be obtained as the eigenvalues of the operator Möbius transformations of Hessenberg matrices and also as the eigenvalues of the operator Möbius transformations of five-diagonal matrices, recently obtained. We illustrate the preceding results with some numerical examples.
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页码：47 / 68
页数：21
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