Smoothing and Approximation of Multivariate Functions

摘要

The goal of the research project was to proceed as far as possible in the study of a certain class of practical approximation problems. Namely, the problem is to reduce the complexity of multivariate functions by representing them precisely or approximately by combinations of univariate functions. A prototype problem is that of finding a best approximation to a function of two variables, F(x,Y), by a sum g(x) + H(y). The prototype problem is thoroughly understood in the case that the functions involved are continuous and an approximation in the uniform sense is needed.