In this paper we study the problem of interpolation on straight lines by linear combinations of a finite number of ridge functions with fixed directions. We analyze in totality the case of one andâ€¦ (More)

The possibility of approximating a continuous function on a compact subset of the real line by a feedforward single hidden layer neural network with a sigmoidal activation function has been studiedâ€¦ (More)

Single hidden layer feedforward neural networks (SLFNs) with fixed weights possess the universal approximation property provided that approximated functions are univariate. But this phenomenon doesâ€¦ (More)

Using two results of Garkavi, Medvedev and Khavinson [7], we give sufficient conditions for proximinality of sums of two ridge functions with bounded and continuous summands in the spaces of boundedâ€¦ (More)

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 thatâ€¦ (More)

Abstract. Let X1, ...,Xn be compact sets and X = X1 Ã— Â· Â· Â·Ã—Xn. Consider the approximation of a function f âˆˆ C(X) by sums g1(x1)+ Â· Â· Â· gn(xn), where gi âˆˆ C(Xi), i = 1, ..., n. In [8], M.Golombâ€¦ (More)