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Chebyshev Polynomials Are Not Always OptimalThe authors are concerned with the problem 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. In this note, the authors show that this is not true in general. Moreover, the authors derive sufficient conditions which guarantee that Chebyshev polynomials are optimal. Also, some numerical examples are presented.
Document ID
19980036961
Acquisition Source
Ames Research Center
Document Type
Thesis/Dissertation
Authors
Fischer, B.
(Stanford Univ. Stanford, CA United States)
Freund, E.
(Stanford Univ. Stanford, CA United States)
Date Acquired
September 6, 2013
Publication Date
June 1, 1989
Subject Category
Astronomy
Report/Patent Number
STAN-CS-89-1264
PB96-150719
NASA/TM-89-206214
NAS 1.15:89-206214
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
Keywords
CHEBYSHEV APPROXIMATION
OPTIMIZATION
POLYNOMIALS

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