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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Original Russian Text © M.A. Komarov, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 9, pp. 28–37.
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Komarov, M.A. An example of non-uniqueness of a simple partial fraction of the best uniform approximation. Russ Math. 57, 22–30 (2013). https://doi.org/10.3103/S1066369X13090041
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DOI: https://doi.org/10.3103/S1066369X13090041