Title
Eigenvalue problems to compute almost optimal points for rational interpolation with prescribed poles Eigenvalue problems to compute almost optimal points for rational interpolation with prescribed poles
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Basel ,
Subject
Mathematics
Source (journal)
Numerical algorithms. - Basel
Volume/pages
45(2007) :1/4 , p. 89-99
ISSN
1017-1398
ISI
000249858000007
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Explicit formulas exist for the (n, m) rational function with monic numerator and prescribed poles that has the smallest possible Chebyshev norm. In this paper we derive two different eigenvalue problems to obtain the zeros of this extremal function. The first one is an ordinary tridiagonal eigenvalue problem based on a representation in terms of Chebyshev polynomials. The second is a generalised tridiagonal eigenvalue problem which we derive using a connection with orthogonal rational functions. In the polynomial case (m = 0) both problems reduce to the tridiagonal eigenvalue problem associated with the Chebyshev polynomials of the first kind.
E-info
https://repository.uantwerpen.be/docman/iruaauth/a5be25/1b02212.pdf
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