Reducing the construction cost of the componentbycomponent construction of good lattice rules
Authors:
J. Dick and F. Y. Kuo
Journal:
Math. Comp. 73 (2004), 19671988
MSC (2000):
Primary 65D30, 65D32; Secondary 68Q25
Published electronically:
August 19, 2003
MathSciNet review:
2059746
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: The construction of randomly shifted rank lattice rules, where the number of points is a prime number, has recently been developed by Sloan, Kuo and Joe for integration of functions in weighted Sobolev spaces and was extended by Kuo and Joe and by Dick to composite numbers. To construct dimensional rules, the shifts were generated randomly and the generating vectors were constructed componentbycomponent at a cost of operations. Here we consider the situation where is the product of two distinct prime numbers and . We still generate the shifts randomly but we modify the algorithm so that the cost of constructing the, now two, generating vectors componentbycomponent is only operations. This reduction in cost allows, in practice, construction of rules with millions of points. The rules constructed again achieve a worstcase strong tractability error bound, with a rate of convergence for .
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Additional Information
J. Dick
Affiliation:
School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia
Email:
josi@maths.unsw.edu.au
F. Y. Kuo
Affiliation:
Department of Mathematics, The University of Waikato, Private Bag 3105, Hamilton, New Zealand
Address at time of publication:
School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia
Email:
fkuo@maths.unsw.edu.au
DOI:
http://dx.doi.org/10.1090/S0025571803016107
PII:
S 00255718(03)016107
Keywords:
QuasiMonte Carlo,
numerical integration,
lattice rules
Received by editor(s):
August 23, 2002
Received by editor(s) in revised form:
February 16, 2003
Published electronically:
August 19, 2003
Article copyright:
© Copyright 2003
American Mathematical Society
