Title: Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules
Authors: Baldeaux, Jan * #
Dick, Josef * #
Leobacher, Gunther * #
Nuyens, Dirk * #
Pillichshammer, Friedrich * # ×
Issue Date: 2012
Publisher: Springer New York LLC
Series Title: Numerical Algorithms vol:59 issue:3 pages:403-431
Abstract: We show how to obtain a fast component-by-component construction algorithm for higher order polynomial lattice rules. Such rules are useful for multivariate quadrature of high-dimensional smooth functions over the unit cube as they achieve the near optimal order of convergence. The main problem addressed in this paper is to find an efficient way of computing the worst-case error. A general algorithm is presented and explicit expressions for base 2 are given. To obtain an efficient component-by-component construction algorithm we exploit the structure of the underlying cyclic group. We compare our new higher order multivariate quadrature rules to existing quadrature rules based on higher order digital nets by computing their worst-case error. These numerical results show that the higher order polynomial lattice rules improve upon the known constructions of quasi-Monte Carlo rules based on higher order digital nets.
ISSN: 1017-1398
Publication status: published
KU Leuven publication type: IT
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
* (joint) first author
× corresponding author
# (joint) last author

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