An example of non-uniqueness of a simple partial fraction of the best uniform approximation |
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Authors: | M A Komarov |
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Institution: | 1. Vladimir State University, ul. Gor’kogo 87, Vladimir, 600000, Russia
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Abstract: | For arbitrary natural n ≥ 2 we construct an example of a real continuous function, for which there exists more than one simple partial fraction of order ≤ n of the best uniform approximation on a segment of the real axis. We prove that even the Chebyshev alternance consisting of n+1 points does not guarantee the uniqueness of the best approximation fraction. The obtained results are generalizations of known non-uniqueness examples constructed for n = 2, 3 in the case of simple partial fractions of an arbitrary order n. |
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