학술논문
The construction of good extensible Korobov rules.
Document Type
Journal
Author
Dick, J. (A-LINZ-IFN) AMS Author Profile; Pillichshammer, F. (5-NSW-SMS) AMS Author Profile; Waterhouse, B. J. AMS Author Profile
Source
Subject
65 Numerical analysis -- 65C Probabilistic methods, simulation and stochastic differential equations
65C05Monte Carlo methods
65Numerical analysis -- 65D Numerical approximation and computational geometry
65D30Numerical integration
65C05
65
65D30
Language
English
Abstract
Summary: ``In this paper, we introduce construction algorithms for Korobov rules for numerical integration which work well for a given set of dimensions simultaneously. The existence of such rules was recently shown by H. Niederreiter\ [Monatsh. Math. {\bf 139} (2003), no.~4, 295--307; MR2001711 (2004j:11087)]. Here we provide a feasible construction algorithm and an upper bound on the worst-case error in certain reproducing kernel Hilbert spaces for such quadrature rules. The proof is based on a sieve principle recently used by the authors to construct extensible lattice rules. We only treat classical lattice rules. The same ideas apply for polynomial lattice rules.''