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.
Highlights
It is well known that the approximation of functions of several variables by simple combinations of univariate functions is of both theoretical and practical significance
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
Summary
It is well known that the approximation of functions of several variables by simple combinations of univariate functions is of both theoretical and practical significance. This type of approximation has arisen, for example, in connection with the classical functional equations [5], the numerical solution of certain elliptic PDE boundary value problems [4], and dimension theory [15]. Where φ(x), ψ(y) are defined and continuous on the projections of Q onto the coordinate axes x and y, respectively.
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