Title
A generalized eigenvalue problem for quasi-orthogonal rational functions A generalized eigenvalue problem for quasi-orthogonal rational functions
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Berlin ,
Subject
Mathematics
Source (journal)
Numerische Mathematik. - Berlin
Volume/pages
117(2011) :3 , p. 463-506
ISSN
0029-599X
ISI
000287145500003
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
In general, the zeros of an orthogonal rational function (ORF) on a subset of the real line, with poles among {alpha(1), ... , alpha(n)} subset of (C(0) boolean OR {infinity}), are not all real (unless alpha(n) is real), and hence, they are not suitable to construct a rational Gaussian quadrature rule (RGQ). For this reason, the zeros of a so-called quasi-ORF or a so-called para-ORF are used instead. These zeros depend on one single parameter tau is an element of (C boolean OR {infinity}), which can always be chosen in such a way that the zeros are all real and simple. In this paper we provide a generalized eigenvalue problem to compute the zeros of a quasi-ORF and the corresponding weights in the RGQ. First, we study the connection between quasi-ORFs, para-ORFs and ORFs. Next, a condition is given for the parameter tau so that the zeros are all real and simple. Finally, some illustrative and numerical examples are given.
E-info
https://repository.uantwerpen.be/docman/iruaauth/9aa6f8/5882904.pdf
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