Title
Good interpolation points : learning from Chebyshev, Fekete, Haar and LebesgueGood interpolation points : learning from Chebyshev, Fekete, Haar and Lebesgue
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Research group
Computational Mathematics
Publication type
article
Publication
New York,
Subject
Mathematics
Source (journal)
AIP conference proceedings / American Institute of Physics. - New York
Volume/pages
1389(2011), p. 1917-1922
ISSN
0094-243X
ISI
000302239800459
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
The search for sets of good interpolation points is highly motivated by the fact that, due to the finite precision of digital computers, valid results can only be expected when the interpolation problem is well‐conditioned. The conditioning of polynomial interpolation and of rational interpolation with preassigned poles is measured by the respective Lebesgue constants. Here we summarize the main results with respect to the Lebesgue constant for polynomial interpolation and we present the best Lebesgue constants in existence for rational interpolation with preassigned poles. The new results are based on a fairly unknown rational analogue of the Chebyshev orthogonal polynomials. We compare with the results obtained in [1] and [2].
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Full text (open access)
https://repository.uantwerpen.be/docman/irua/cb25d6/107036.pdf
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