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Title
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A generalized eigenvalue problem for quasi-orthogonal rational functions
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Author
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Abstract
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| 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. |
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Language
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English
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Source (journal)
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Numerische Mathematik. - Berlin
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Publication
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Berlin
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2011
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ISSN
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0029-599X
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DOI
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10.1007/S00211-010-0356-X
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Volume/pages
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117
:3
(2011)
, p. 463-506
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ISI
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000287145500003
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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