Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9501287 | Journal of Complexity | 2005 | 15 Pages |
Abstract
We study the worst-case error of quasi-Monte Carlo (QMC) rules for multivariate integration in some weighted Sobolev spaces of functions defined on the product of d copies of the unit sphere SsâRs+1. The space is a tensor product of d reproducing kernel Hilbert spaces defined in terms of uniformly bounded 'weight' parameters γd,j for j=1,2,â¦,d. We prove that strong QMC tractability holds (i.e. the number of function evaluations needed to reduce the initial error by a factor of É is bounded independently of d) if and only if limsupdâââj=1dγd,j<â; and tractability holds (i.e. the number of function evaluations grows at most polynomially in d) if and only if limsupdâââj=1dγd,j/log(d+1)<â. The arguments are not constructive.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Frances Y. Kuo, Ian H. Sloan,