Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces
SIAM Journal on Numerical Analysis
Component-by-component construction of good lattice rules
Mathematics of Computation
Journal of Complexity
Open problems for tractability of multivariate integration
Journal of Complexity
On the convergence rate of the component-by-component construction of good lattice rules
Journal of Complexity
Journal of Complexity
Quasi-Monte Carlo methods can be efficient for integration over products of spheres
Journal of Complexity
Randomly shifted lattice rules for unbounded integrands
Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005
Weighted intermediate rank lattice rules with applications in finance
MOAS'07 Proceedings of the 18th conference on Proceedings of the 18th IASTED International Conference: modelling and simulation
Intermediate rank lattice rules and applications to finance
Applied Numerical Mathematics
Weighted intermediate rank lattice rules with applications in finance
MS '07 The 18th IASTED International Conference on Modelling and Simulation
Variance bounds and existence results for randomly shifted lattice rules
Journal of Computational and Applied Mathematics
Constructing adapted lattice rules using problem-dependent criteria
Proceedings of the Winter Simulation Conference
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We develop algorithms to construct rank-1 lattice rules in weighted Korobov spaces of periodic functions and shifted rank-1 lattice rules in weighted Sobolev spaces of non-periodic functions. Analyses are given which show that the rules so constructed achieve strong QMC tractability error bounds. Unlike earlier analyses, there is no assumption that n, the number of quadrature points, be a prime number. However, we do assume that there is an upper bound on the number of distinct prime factors of n. The generating vectors and shifts characterizing the rules are constructed 'component-by-component,' that is, the (d+ 1)th components of the generating vectors and shifts are obtained using one-dimensional searches, with the previous d components kept unchanged.