Algorithms reconstructing the iterated functional which are optimal in classes of grid products (Q1103321)

Given a class of functions f(x,y) defined on \(X\times Y\), functionals of the form \(U(f)=U_ X(U_ Y(x)(f))\) are introduced, where \(U_ X:{\mathcal F}\to R\), \(U_ Y: F_ y\to {\mathbb{R}}\), \({\mathcal F}_ x\), \({\mathcal F}_ y\) being classes of functions. The author considers the problem of approximation of U in a certain optimal way on the basis of the values of f at a given number of points from \(X\times Y\).