Publication
Title
Eigenvalue problems to compute almost optimal points for rational interpolation with prescribed poles
Author
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.
Language
English
Source (journal)
Numerical algorithms. - Basel
Publication
Basel : 2007
ISSN
1017-1398
Volume/pages
45:1/4(2007), p. 89-99
ISI
000249858000007
Full text (Publisher's DOI)
Full text (publisher's version - intranet only)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 12.07.2012
Last edited 28.10.2017
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