Approximating by Ridge Functions

. This paper surveys certain aspects of the study of ridge functions. We hope it will also encourage some readers to consider researching problems in this area. After first explaining what ridge functions are and giving various motivations for their study, we turn to the problem of presenting algorithms for approximating by ridge functions. We then touch upon the topic of determining the degree of approximation by ridge functions, and that of recognizing functions which are linear combinations of ridge functions. x1. Introduction This short paper is an introduction to certain aspects of the study of ridge functions. After first explaining what ridge functions are and giving various motivations for their study, we turn to the problem of presenting algorithms for approximating by ridge functions. We then touch upon the topic of determining the degree of approximation by ridge functions, and that of recognizing when we have a function which is a linear combination of ridge functions. Thi..