Author(s)

N.K. Dicheva

Abstract

The problem of the best recovery in a sense of Sard of linear functional Lf, f £ W| [a, b] -Sobolev space, on the basis of information T(f) = {(L^/j, j = 1, 2,..., n} is considered. It is shown that this leads to the best ap- proximation of LK in the space 5 = span{LjK}, j = 1,2,..., n, where K — (x —£)+" /(q — 1)! is a truncated power kernel. This problem is solved using Gramm-Schmidt orthogonalization and the best recovery of Lf is ob- tained in analytical form. Two applications are considered - interpolation of a function on the basis of given values in some points and of given local mean values. The solutions are given in analytical form which differs from the solutions obtained after solving linear systems. It is shown

Keywords