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Strong tractability of multivariate integration of arbitrary order
Author(s) -
Dick Josef,
Pillichshammer Friedrich
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700276
Subject(s) - sobolev space , smoothness , mathematics , lattice (music) , order (exchange) , convergence (economics) , rate of convergence , multivariate statistics , degree (music) , polynomial , pure mathematics , combinatorics , mathematical analysis , computer science , physics , statistics , economics , telecommunications , channel (broadcasting) , finance , acoustics , economic growth
We show the existence of digitally‐shifted polynomial lattice rules which achieve strong tractability results for Sobolev spaces of arbitrary high smoothness. The convergence rate is shown to be best possible up to a given degree of smoothness of the integrand. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)