Dependence on the Dimension for Complexity of Approximation of Random Fields
Abstract
We consider an \eps-approximation by n-term partial sums of the Karhunen-Lo\`eve expansion to d-parametric random fields of tensor product-type in the average case setting. We investigate the behavior, as d tends to infinity, of the information complexity n(\eps,d) of approximation with error not exceeding a given level \eps. It was recently shown by M.A. Lifshits and E.V. Tulyakova that for this problem one observes the curse of dimensionality (intractability) phenomenon. The aim of this paper is to give the exact asymptotic expression for the information complexity n(\eps,d).
Cite
@article{arxiv.math/0701058,
title = {Dependence on the Dimension for Complexity of Approximation of Random Fields},
author = {N. Serdyukova},
journal= {arXiv preprint arXiv:math/0701058},
year = {2012}
}
Comments
18 pages. The published in Theory Probab. Appl. (2010) extended English translation of the original paper "Zavisimost slozhnosti approximacii sluchajnyh polej ot rasmernosti", submitted on 15.01.2007 and published in Theor. Veroyatnost. i Primenen. 54:2, 256-270