Abstract

It is known that the generating vector of a rank-1 lattice rule can be constructed component-by-component to achieve strong tractability error bounds in both weighted Korobov spaces and weighted Sobolev spaces. Since the weights for these spaces are nonincreasing, the first few variables are in a sense more important than the rest. We thus propose to copy the points of a rank-1 lattice rule a number of times in the first few dimensions to yield an intermediate-rank lattice rule. We show that the generating vector (and in weighted Sobolev spaces, the shift also) of an intermediate-rank lattice rule can also be constructed component-by-component to achieve strong tractability error bounds. In certain circumstances, these bounds are better than the corresponding bounds for rank-1 lattice rules.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call