On The Best Recovery Of Linear Functional And
Its Applications
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
Related Book
Other papers in this volume
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