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An overview of fast component‐by‐component constructions of lattice rules and lattice sequences
Author(s) -
Nuyens Dirk,
Cools Ronald
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700919
Subject(s) - lattice (music) , component (thermodynamics) , sketch , mathematics , multivariate statistics , computer science , combinatorics , algorithm , physics , statistics , quantum mechanics , acoustics
Since the initial work by I. H. Sloan and his collaborators on the component‐by‐component construction of good lattice rules for the approximation of multivariate integrals, a lot of variations on this theme have been published. These include various function spaces, prime and composite number of points, intermediate‐rank rules, polynomial lattice rules and extensible rules. We sketch the different variations and discuss the properties needed to have a fast component‐by‐component construction. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)