On approximation by ridge functions (Q1381501)

Ridge functions are defined as functions of the form \(f(ax)\), where \(f:\mathbb{R}\to\mathbb{R}\), \(x\in\mathbb{R}^k\), a belongs to a given ``direction'' set \(A\subset R^k\) and \(ax\) stands for the inner product. Such functions arise in connection with computerized tomography, neural networks, and other areas of applied mathematics. The author studies some aspects of approximation by ridge functions, in particular the fundamentality of these functions for variable direction sets and the rate of approximation by ridge functions.