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

Journal Article · Mon Oct 01 04:00:00 EDT 2001 · Math. Comput.

DOI:https://doi.org/10.1090/S0025-5718-01-01326-6· OSTI ID:942776

Cools, R; Lyness, J N

A systematic search for optimal lattice rules of specified trigonometric degree d over the hypercube (0,1){sup s} has been undertaken. The search is restricted to a population K(s,{delta}) of lattice rules Q(A). This includes those where the dual lattice {Lambda}{perpendicular} may be generated by s points h for each of which |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 < 29 and s = 4, d {<=} 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.

• Research Organization: Argonne National Laboratory (ANL)
• Sponsoring Organization: SC
• DOE Contract Number: AC02-06CH11357
• OSTI ID: 942776
• Report Number(s): ANL/MCS/JA-34530
• Journal Information: Math. Comput., Journal Name: Math. Comput. Journal Issue: 236 ; Oct. 2001 Vol. 70; ISSN 0025-5718; ISSN MCMPAF
• Country of Publication: United States
• Language: ENGLISH

Related Subjects

97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
CALCULATION METHODS
COMPUTER CALCULATIONS
FOUR-DIMENSIONAL CALCULATIONS
THREE-DIMENSIONAL CALCULATIONS