International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 65620, 11 pages
On error formulas for approximation by sums of univariate functions
Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, 9 F. Agaev Street, Baku 1141, Azerbaijan
Received 8 February 2005; Revised 1 December 2005; Accepted 12 March 2006
Copyright © 2006 Vugar E. Ismailov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The purpose of the paper is to develop a new method for obtaining
explicit formulas for the error of approximation of bivariate
functions by sums of univariate functions. It should be remarked
that formulas of this type have been known only for functions
defined on a rectangle with sides parallel to coordinate axes. Our
method, based on a maximization process over closed bolts, allows
the consideration of functions defined on a hexagon or octagon
with sides parallel to coordinate axes.