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Constructions of general polynomial lattices for multivariate integration

Published online by Cambridge University Press:  17 April 2009

Peter Kritzer  and
Friedrich Pillichshammer
Peter Kritzer
Affiliation:
Fachbereich Mathematik, Universität Salzburg, Hellbrunnerstr. 34, A-5020 Salzburg, Austria, e-mail: peter.kritzer@sbg.ac.at
Friedrich Pillichshammer
Affiliation:
Institut für Finanzmathematik, Universität Linz, Altenbergerstr. 69, A-4040 Linz, Austria, e-mail: friedrich.pillichshammer@jku.at
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We study a construction algorithm for certain polynomial lattice rules modulo arbitrary polynomials. The underlying polynomial lattices are special types of digital nets as introduced by Niederreiter. Dick, Kuo, Pillichshammer and Sloan recently introduced construction algorithms for polynomial lattice rules modulo irreducible polynomials which yield a small worst-case error for integration of functions in certain weighted Hilbert spaces. Here, we generalize these results to the case where the polynomial lattice rules are constructed modulo arbitrary polynomials.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 76 , Issue 1 , August 2007 , pp. 93 - 110
Copyright
Copyright © Australian Mathematical Society 2007

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