Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces

  • Authors:

  • I. H. Sloan;F. Y. Kuo;S. Joe

  • Affiliations:

  • -;-;-

  • Venue:
  • SIAM Journal on Numerical Analysis
  • Year:
  • 2002

Quantified Score

Hi-index 0.01

Visualization

Abstract

Shifted rank-1 lattice rules, a special class of quasi-Monte Carlo methods, have recently been proposed by the present authors for the integration of functions belonging to certain "weighted" Sobolev spaces. The shifts in these rules were generated in a deterministic manner. In contrast, in this paper we generate these shifts randomly. This allows probabilistic estimates for the error in a given integral. It also reduces the number of operations required to find the generating vectors for the underlying lattice rules component-by-component. The rules thus constructed achieve a worst-case strong tractability error bound in an average or probabilistic sense.