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- Title
Sufficient condition for the best uniform approximation by simple partial fractions.
- Authors
Komarov, M.
- Abstract
Under the assumption that a certain algebraic identity holds for all $ n\in \mathbb{N} $ (it is verified for n ≤ 5), we prove that a real-valued simple partial fraction R with n simple poles lying outside the unit disk is a simple partial fraction of degree at most n of the best uniform approximation of a continuous real-valued functions f on [−1, 1] provided that for the difference f − R there is a Chebyshev alternance of n + 1 points on [−1, 1]. The result is applied to the problem of approximation of real constants. Bibliography: 8 titles.
- Subjects
APPROXIMATION theory; PARTIAL fractions; MATHEMATICAL proofs; MATHEMATICAL constants; CONTINUOUS functions; MATHEMATICAL analysis; NUMERICAL analysis
- Publication
Journal of Mathematical Sciences, 2013, Vol 189, Issue 3, p482
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-013-1201-4