Component-by-component construction of good lattice rules

Authors:
I. H. Sloan and A. V. Reztsov

Journal:
Math. Comp. **71** (2002), 263-273

MSC (2000):
Primary 65D30, 65D32

DOI:
https://doi.org/10.1090/S0025-5718-01-01342-4

Published electronically:
October 4, 2001

MathSciNet review:
1862999

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper provides a novel approach to the construction of good lattice rules for the integration of Korobov classes of periodic functions over the unit -dimensional cube. Theorems are proved which justify the construction of good lattice rules one component at a time - that is, the lattice rule for dimension is obtained from the rule for dimension by searching over all possible choices of the th component, while keeping all the existing components unchanged. The construction, which goes against accepted wisdom, is illustrated by numerical examples. The construction is particularly useful if the components of the integrand are ordered, in the sense that the first component is more important than the second, and so on.

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Additional Information

**I. H. Sloan**

Affiliation:
School of Mathematics, University of New South Wales, Sydney, New South Wales 2052, Australia

Email:
i.sloan@unsw.edu.au

**A. V. Reztsov**

Affiliation:
School of Mathematics, University of New South Wales, Sydney, New South Wales 2052, Australia

DOI:
https://doi.org/10.1090/S0025-5718-01-01342-4

Received by editor(s):
May 5, 2000

Published electronically:
October 4, 2001

Article copyright:
© Copyright 2001
American Mathematical Society