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Chebyshev polynomials are not always optimalThe problem is that of finding among all polynomials of degree at most n and normalized to be 1 at c the one with minimal uniform norm on Epsilon. Here, Epsilon is a given ellipse with both foci on the real axis and c is a given real point not contained in Epsilon. Problems of this type arise in certain iterative matrix computations and, in this context, it is generally believed and widely referenced that suitably normalized Chebyshev polynomials are optimal for such constrained approximation problems. It is shown that this is not true in general. Moreover, sufficient conditions are derived which guarantee that Chebyshev polynomials are optimal. Some numerical examples are also presented.
Document ID
19900014692
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Fischer, Bernd
(Hamburg Univ. (Germany F.R.)., United States)
Freund, Roland
(Wuerzburg Univ. Germany, F.R. , United States)
Date Acquired
September 6, 2013
Publication Date
April 1, 1989
Subject Category
Numerical Analysis
Report/Patent Number
RIACS-TR-89.17
NASA-CR-181465
NAS 1.26:181465
Accession Number
90N24008
Funding Number(s)
CONTRACT_GRANT: NCC2-387
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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