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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2012, Volume 8, Number 1, Pages 63–78
(Mi jmag525)
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Elementary solutions of the Bernstein problem on two intervals
F. Pausinger I.S.T. Austria, Am Campus 1, A-3400 Klosterneuburg, Austria
Abstract:
First we note that the best polynomial approximation to $|x|$ on the set, which consists of an interval on the positive half-axis and a point on the negative half-axis, can be given by means of the classical Chebyshev polynomials. Then we explore the cases when a solution of the related problem on two intervals can be given in elementary functions.
Key words and phrases:
Chebyshev polynomials, polynomial approximation of $|x|$, Bernstein problem.
Received: 31.08.2011
Citation:
F. Pausinger, “Elementary solutions of the Bernstein problem on two intervals”, Zh. Mat. Fiz. Anal. Geom., 8:1 (2012), 63–78
Linking options:
https://www.mathnet.ru/eng/jmag525 https://www.mathnet.ru/eng/jmag/v8/i1/p63
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Abstract page: | 229 | Full-text PDF : | 78 | References: | 30 |
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