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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, Number 8, Pages 67–79
(Mi ivm9270)
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This article is cited in 14 scientific papers (total in 14 papers)
Polynomials orthogonal in the Sobolev sense, generated by Chebyshev polynomials orthogornal on a mesh
I. I. Sharapudinovab, T. I. Sharapudinovcb a Daghestan State Pedagogical University
b Dagestan Scientific Center of the Russian Academy of Sciences,
17 Gamidov str., Makhachkala, 367013 Russia
c Vladikavkaz Scientific Center of the Russian Academy of Sciences,
45 Gadzhiev str., Makhachkala, 367023 Russia
Abstract:
We consider the problem of constructing polynomials, orthogonal in Sobolev sense on the finite uniform mesh and associated with classical Chebyshev polynomials of discrete variable. We have found an explicit expression of these polynomials by classical Chebyshev polynomials. Also we have obtained an expansion of new polynomials by generalized powers of Newton type. We obtain expressions for the deviation of a discrete function and its finite differences from respectively partial sums of its Fourier series on the new system of polynomials and their finite differences.
Keywords:
polynomials orthogonal in Sobolev sence, Chebyshev polynomials orthogonal on the mesh, approximation of discrete functions, mixed series of Chebyshev polynomials orthogonal on a uniform mesh.
Received: 18.04.2016
Citation:
I. I. Sharapudinov, T. I. Sharapudinov, “Polynomials orthogonal in the Sobolev sense, generated by Chebyshev polynomials orthogornal on a mesh”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 8, 67–79; Russian Math. (Iz. VUZ), 61:8 (2017), 59–70
Linking options:
https://www.mathnet.ru/eng/ivm9270 https://www.mathnet.ru/eng/ivm/y2017/i8/p67
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Abstract page: | 301 | Full-text PDF : | 59 | References: | 32 | First page: | 24 |
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