On a Lebesgue constant of interpolation rational process at the Chebyshev – Markov nodes

  • Yauheni A. Rouba Yanka Kupala State University of Grodno, 22 Ažeška Street, Grodno 230023, Belarus
  • Kanstantin A. Smatrytski Yanka Kupala State University of Grodno, 22 Ažeška Street, Grodno 230023, Belarus
  • Yauheni V. Dirvuk Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, 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.

Author Biographies

Yauheni A. Rouba, Yanka Kupala State University of Grodno, 22 Ažeška Street, Grodno 230023, Belarus

doctor of science (physics and mathematics), full professor; head of the department of fundamental and applied mathematics, faculty of mathematics and informatics

Kanstantin A. Smatrytski, Yanka Kupala State University of Grodno, 22 Ažeška Street, Grodno 230023, Belarus

PhD (physics and mathematics), docent; associate professor at the department of fundamental and applied mathematics, faculty of mathematics and informatics

Yauheni V. Dirvuk, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

PhD (physics and mathematics); associate professor at the department of system programming and computer security, faculty of mathematics and informatics

References

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  6. Rouba YA, Kazlouskaya NY. [On a problem of estimation of a Lebesgue constant of interpolation rational processes at the Chebyshev – Markov nodes]. Vesnik Hrodzenskaha dziarzhaunaha universiteta imia Ianki Kupaly. Seriya 2. 2016;6(3):6 –11. Russian.
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Published
2019-01-19
Keywords: rational approximation, interpolation, Chebyshev – Markov fraction, Lebesgue constant
How to Cite
Rouba, Y. A., Smatrytski, K. A., & Dirvuk, Y. V. (2019). On a Lebesgue constant of interpolation rational process at the Chebyshev – Markov nodes. Journal of the Belarusian State University. Mathematics and Informatics, 3, 12-20. Retrieved from https://journals.bsu.by/index.php/mathematics/article/view/1008
Issue
No 3 (2018): Journal of the Belarusian State University. Mathematics and Informatics
Section
Real, Complex and Functional Analysis

Copyright (c) 2018 Journal of the Belarusian State University. Mathematics and Informatics

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