Characterization of an extremal sum of ridge functions

Abstract

The approximation problem considered in the paper is to approximate a continuous multivariate function f ( x ) = f ( x 1 , … , x d ) by sums of two ridge functions in the uniform norm. We give a necessary and sufficient condition for a sum of two ridge functions to be a best approximation to f ( x ) . This main result is next used in a special case to obtain an explicit formula for the approximation error and to construct one best approximation. The problem of well approximation by such sums is also considered.