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Journal of the Belarusian State University. Mathematics and Informatics, 2018, Volume 3, Pages 12–20
(Mi bgumi115)
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Real, Complex and Functional analysis
On a Lebesgue constant of interpolation rational process at the Chebyshev – Markov nodes
Y. A. Rovba, K. A. Smotritskii, E. V. Dirvuk Yanka Kupala State University of Grodno, 22 Ažeška Street, Grodno 230023, Belarus
Abstract:
In the present paper estimate of a Lebesgue constant of the interpolation rational Lagrange process on the segment $[-1,1]$, at the Chebyshev – Markov cosine fractions nodes is considered. It is shown that in the case of two real geometrically distinct poles of approximating functions, the norms of the Lagrange fundamental polynomials are bounded. Based on this result, it is proved that in the case under consideration the upper estimate of the Lebesgue constant does not depend on the arrangement of the poles and the sequence of the Lebesgue constant grows with logarithmic rate. Note, that in previous works the estimates of Lebesgue constants were obtained only for particular choices of poles or depended on the arrangement of poles.
Keywords:
rational approximation; interpolation; Chebyshev – Markov fraction; Lebesgue constant.
Received: 28.06.2018
Citation:
Y. A. Rovba, K. A. Smotritskii, E. V. Dirvuk, “On a Lebesgue constant of interpolation rational process at the Chebyshev – Markov nodes”, Journal of the Belarusian State University. Mathematics and Informatics, 3 (2018), 12–20
Linking options:
https://www.mathnet.ru/eng/bgumi115 https://www.mathnet.ru/eng/bgumi/v3/p12
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Abstract page: | 55 | Full-text PDF : | 19 | References: | 18 |
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