This article is cited in 3 papers

Estimate of the Norm of the Lagrange Interpolation Operator in a Multidimensional Sobolev Space

A. I. Fedotov

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University

Abstract: We obtain an estimate of the norm of the Lagrange interpolation operator in a multidimensional Sobolev space. It is shown that, under a suitable choice of the sequence of multi-indices, interpolation polynomials converge to the interpolated function and their rate of convergence is of the order of the best approximation of this function.

Keywords: Lagrange interpolation operator, interpolation polynomial, rate of convergence, best approximation, Sobolev space, Hilbert space.

UDC: 517.518.823

Received: 16.06.2003
Revised: 29.05.2006

DOI: 10.4213/mzm3684

 English version: Mathematical Notes, 2007, 81:3, 373–378

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