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A generalized eigenvalue problem for quasi-orthogonal rational functions
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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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English
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Numerische Mathematik. - Berlin | |
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Berlin : 2011
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0029-599X
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117:3(2011), p. 463-506
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000287145500003
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