Estimate of the norm of the Lagrange interpolation operator in the multidimensional weighted Sobolev space

被引：0

作者：

A. I. Fedotov

机构：

[1] Kazan Federal University,

来源：

Mathematical Notes | 2016年 / 99卷

关键词：

Lagrange interpolation operator; weighted Sobolev space; interpolating polynomials; approximation by algebraic polynomials; Chebyshev polynomials; Fourier coefficients of a polynomial;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

An estimate of the norm of the Lagrange interpolation operator in the multidimensional weighted Sobolev space is obtained. It is shown that, under a certain choice of the sequence of multi-indices, the interpolating polynomials converge to the interpolated function and the rate of convergence is of the order of the best approximation of this function by algebraic polynomials in this space.

引用

页码：747 / 756

页数：9

共 8 条

[1]

Gabdulkhaev B. G.(1975)Approximation in H-spaces and applications Dokl. Akad. Nauk SSSR 223 1293-1296

[2]

Amosov B. A.(1990)On the approximate solution of elliptic pseudodifferential equations on a smooth closed curve Z. Anal. Andwen. 9 545-563

[3]

Gabdulkhaev B. G.(1997)The Lagrange interpolation polynomials in Sobolev spaces Izv. Vyssh. Uchebn. Zaved. Mat. 5 7-19

[4]

Ermolaeva L. B.(1998)Fast solvers of integral and pseudodifferential equations on closed curves Math. Comp. 67 1473-1491

[5]

Saranen J.(2007)An estimate of the norm of the Lagrange interpolation operator in a multidimensional Sobolev space Mat. Zametki 81 427-433

[6]

Vainikko G.(2004)Convergence of cubature-differencesmethod for multidimensional singular integro-differential equations Arch.Math. (Brno) 40 181-191

[7]

Fedotov A. I.(undefined)undefined undefined undefined undefined-undefined

[8]

Fedotov A. I.(undefined)undefined undefined undefined undefined-undefined

← 1 →