Characterization of an extremal sum of ridge functions

Authors:
Vugar E. Ismailov
Affiliations:
Mathematics and Mechanics Institute, Azerbaijan National Academy of Sciences, Az-1141, Baku, Azerbaijan
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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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.