Title: Fast component-by-component construction of rank-1 lattice rules with a non-prime number of points
Authors: Nuyens, Dirk ×
Cools, Ronald #
Issue Date: Feb-2006
Publisher: Elsevier
Series Title: Journal of Complexity vol:22 issue:1 pages:4-28
Abstract: The component-by-component construction algorithm constructs the generating vector for a rank-1 lattice one component at a time by minimizing the worst-case error in each step. This algorithm can be formulated elegantly as a repeated matrix-vector product, where the matrix-vector product expresses the calculation of the worst-case error in that step. As was shown in an earlier paper, this matrix-vector product can be done in time O(n log (n)) and with memory O(n) when the number of points n is prime. Here we extend this result to general n to obtain a total construction cost of O(sn log (n)) and memory of O(n) for a rank-1 lattice in s dimensions with n points. We thus obtain the same big-Oh result as for n prime.
ISSN: 0885-064X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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