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Title: A generalized eigenvalue problem for quasi-orthogonal rational functions
Authors: Deckers, Karl ×
Bultheel, Adhemar
Van Deun, Joris #
Issue Date: Mar-2011
Publisher: Springer
Series Title: Numerische Mathematik vol:117 issue:3 pages:463-506
Abstract: In general, the zeros of an orthogonal rational function (ORF) on a subset of the real line, with poles among {α1, . . . , αn} ⊂ (ℂ0∪{∞}), are not all real (unless αn 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 (qORF) or a so-called para-ORF (pORF) are used instead. These zeros depend on one single parameter τ ∈ (ℂ ∪ {∞}), 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 qORFs, pORFs and ORFs. Next, a condition is given for the parameter τ so that the zeros are all real and simple. Finally, some illustrative and numerical examples are given.
URI: 
ISSN: 0029-599X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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