Polynomials orthogonal in the Sobolev sense, generated by Chebyshev polynomials orthogonal on a mesh

被引：5

作者：

Sharapudinov I.I. ^{[1
]}

Sharapudinov T.I. ^{[2
]}

机构：

[1] Dagestan State Pedagogical University, Dagestan Scientific Center of the Russian Academy of Sciences, ul. Gamidova 17, Makhachkala

[2] Dagestan Scientific Center of the Russian Academy of Sciences, Vladikavkaz Scientific Center of the Russian Academy of Sciences, ul. Gadzhieva 45, Makhachkala

来源：

Russian Mathematics | 2017年 / 61卷 / 8期

关键词：

approximation of discrete functions; Chebyshev polynomials orthogonal on the mesh; mixed series of Chebyshev polynomials orthogonal on a uniform mesh; polynomials orthogonal in Sobolev sence;

D O I：

10.3103/S1066369X17080072

中图分类号：

学科分类号：

摘要：

We consider the problem of constructing polynomials, orthogonal in the 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 classicalChebyshev polynomials. Also we have obtained an expansion of new polynomials by generalized powers ofNewton 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. © 2017, Allerton Press, Inc.

引用

页码：59 / 70

页数：11

共 15 条

[1]

Iserles A., Koch P.E., Norsett S.P., Sanz-Serna J.M., On PolynomialsOrthogonal with Respect to Certain Sobolev Inner Products, J. Approx. Theory, 65, pp. 151-175, (1991)

[2]

Marcellan F., Alfaro M., Rezola M.L., Orthogonal Polynomials on Sobolev Spaces: Old and New Directions, Journal of Computational and AppliedMathematics, 48, pp. 113-131, (1993)

[3]

Meijer H.G., Laguerre Polynomials Generalized to a Certain Discrete Sobolev Inner Product Space, J. Approx. Theory, 73, pp. 1-16, (1993)

[4]

Kwon K.H., Littlejohn L.L., The Orthogonality of the Laguerre Polynomials L <sub>n</sub> <sup>(-k)</sup> (x) for Positive Integers k, Ann. Numer. Anal., 2, pp. 289-303, (1995)

[5]

Kwon K.H., Littlejohn L.L., Sobolev Orthogonal Polynomials and Second-order Differential Equations, Rocky Mountain J. Math., 28, pp. 547-594, (1998)

[6]

Marcellan F., Yuan X., On SobolevOrthogonal Polynomials, 2014, pp. 1-40, (2014)

[7]

Sharapudinov I.I., Mixed Series in Chebyshev Polynomials that are Orthogonal on a Uniform Grid, Math. Notes, 78, 3-4, pp. 403-423, (2005)

[8]

Sharapudinov I.I., Sharapudinov T.I., Mixed Series in Jacobi and Chebyshev Polynomials and their Discretization, Math.Notes, 88, 1-2, pp. 112-139, (2010)

[9]

Trefethen L.N., Spectral Methods in Matlab, (2000)

[10]

Trefethen L.N.F., Difference and SpectralMethods for Ordinary and Partial Differential Equation, (1996)

← 1 2 →