Kuo, F.Y. & Joe, S.(2003). Component-by-component construction of good intermediate-rank lattice rules. SIAM Journal of Numerical Analysis, 41(4), 1465-1486.
Permanent Research Commons link: http://hdl.handle.net/10289/1740
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.
Society for Industrial and Applied Mathematics
This is an author’s version of an article published in the journal: SIAM Journal of Numerical Analysis. © 2003 Society for Industrial and Applied Mathematics. Used with permission.