The index of merit of kth-copy integration lattices

Authors:
Tiancheng Li;Ian Robinson;Michael Hill
Affiliations:
Department of Computer Science and Computer Engineering, La Trobe University, Bundoora, VIC 3086, Australia;Department of Computer Science and Computer Engineering, La Trobe University, Bundoora, VIC 3086, Australia;Department of Computer Science and Computer Engineering, La Trobe University, Bundoora, VIC 3086, Australia
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

r2d2lri is an automatic two-dimensional cubature algorithm that demonstrates the practical value of using an augmentation sequence consisting of (2^k)^2-copy lattices as a basis for numerical integration. This paper investigates use of similar embedded augmentation sequences in higher dimensions by developing theoretical results relating to the index of merit of s-dimensional (2^k)^s-copy lattices generated from rank-1 simple lattices. The theoretical results can be used to guide the search for good augmentation sequences in s dimensions in the sense of high index of merit.