Title




A generalized eigenvalue problem for quasiorthogonal rational functions
 
Author




 
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 socalled quasiORF or a socalled paraORF 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 quasiORF and the corresponding weights in the RGQ. First, we study the connection between quasiORFs, paraORFs 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. 
 
Language




English
 
Source (journal)




Numerische Mathematik.  Berlin
 
Publication




Berlin
:
2011
 
ISSN




0029599X
 
DOI




10.1007/S002110100356X
 
Volume/pages




117
:3
(2011)
, p. 463506
 
ISI




000287145500003
 
Full text (Publisher's DOI)




 
Full text (publisher's version  intranet only)




 
