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

Abstract

© 2016, Pleiades Publishing, Ltd.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.