Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773839 | Journal of Complexity | 2017 | 22 Pages |
Abstract
We introduce a new notion of tractability for multivariate problems, namely (s,lnκ)-weak tractability for positive s and κ. This allows us to study the information complexity of a d-variate problem with respect to different powers of d and the bits of accuracy lnεâ1. We consider the worst case error for the absolute and normalized error criteria. We provide necessary and sufficient conditions for (s,lnκ)-weak tractability for general linear problems and linear tensor product problems defined over Hilbert spaces. In particular, we show that non-trivial linear tensor product problems cannot be (s,lnκ)-weakly tractable when sâ(0,1] and κâ(0,1]. On the other hand, they are (s,lnκ)-weakly tractable for κ>1 and s>1 if the univariate eigenvalues of the linear tensor product problem enjoy a polynomial decay. Finally, we study (s,lnκ)-weak tractability for the remaining combinations of the values of s and κ.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
A. Papageorgiou, I. Petras, H. Woźniakowski,