Dependence on the Dimension for Complexity of Approximation of Random Fields (in Russian)

Abstract

In the present paper a behavior of the "average case" approximation complexity for d-parametric random fields of tensor-type is studied. It was shown in [Lifshits and Tulyakova, 2006] that for a given approximation accuracy level the complexity of approximation increases exponentially, as d tends to infinity; that is the curse of dimensionality is observed. In this paper a technique allowing obtaining sharp asymptotic expressions for the approximation complexity is developed and such an expression is obtained.