International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 1, Article ID 65620, 11 pages
doi:10.1155/IJMMS/2006/65620
On error formulas for approximation by sums of univariate functions
Vugar E. Ismailov
Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, 9 F. Agaev Street, Baku 1141, Azerbaijan
Abstract
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.