Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Three- and four-dimensional $K$-optimal lattice rules of moderate trigonometric degree

Authors: Ronald Cools and James N. Lyness
Journal: Math. Comp. 70 (2001), 1549-1567
MSC (2000): Primary 41A55, 41A63, 42A10; Secondary 65D32
Published electronically: May 14, 2001
MathSciNet review: 1836918
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A systematic search for optimal lattice rules of specified trigonometric degree $d$ over the hypercube $[0,1)^s$ has been undertaken. The search is restricted to a population $K(s,\delta )$ of lattice rules $Q(\Lambda )$. This includes those where the dual lattice $\Lambda ^\perp$ may be generated by $s$ points $\bf h$ for each of which $|\textbf {h} | = \delta =d+1$. The underlying theory, which suggests that such a restriction might be helpful, is presented. The general character of the search is described, and, for $s=3$, $d \leq 29$ and $s=4$, $d \leq 23$, a list of $K$-optimal rules is given. It is not known whether these are also optimal rules in the general sense; this matter is discussed.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 41A55, 41A63, 42A10, 65D32

Retrieve articles in all journals with MSC (2000): 41A55, 41A63, 42A10, 65D32

Additional Information

Ronald Cools
Affiliation: Department of Computer Science, K. U. Leuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium
MR Author ID: 51325
ORCID: 0000-0002-5567-5836

James N. Lyness
Affiliation: Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439 and School of Mathematics, University of New South Wales, Sydney 2052 Australia

Received by editor(s): November 29, 1999
Published electronically: May 14, 2001
Additional Notes: The second author was supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, U.S. Dept. of Energy, under Contract W-31-109-Eng-38.
Article copyright: © Copyright 2001 University of Chicago and Katholieke Universiteit Leuven