Component by Component Construction of Rank-1 Lattice Rules HavingO(n -1(In(n))d) Star Discrepancy

2004 ◽  
pp. 293-298 ◽  
Author(s):  
Stephen Joe
Keyword(s):  
Lattice Rules ◽  
Star Discrepancy

scholarly journals Constructions of general polynomial lattice rules based on the weighted star discrepancy

2007 ◽  
Vol 13 (4) ◽  
pp. 1045-1070 ◽  
Author(s):  
Josef Dick ◽  
Peter Kritzer ◽  
Gunther Leobacher ◽  
Friedrich Pillichshammer
Keyword(s):  
Lattice Rules ◽  
General Polynomial ◽  
Star Discrepancy

scholarly journals Good lattice rules based on the general weighted star discrepancy

2006 ◽  
Vol 76 (258) ◽  
pp. 989-1004 ◽  
Author(s):  
Vasile Sinescu ◽  
Stephen Joe
Keyword(s):  
Lattice Rules ◽  
Good Lattice ◽  
Star Discrepancy

scholarly journals The number of lattice rules having given invariants

1992 ◽  
Vol 46 (3) ◽  
pp. 479-495 ◽  
Author(s):  
Stephen Joe ◽  
David C. Hunt
Keyword(s):  
Normal Form ◽  
Quadrature Rule ◽  
Unit Cube ◽  
Numerical Results ◽  
Smith Normal Form ◽  
Lattice Rules ◽  
Dimensional Unit ◽  
Lattice Rule ◽  
Positive Integers ◽  
Theoretical Results

A lattice rule is a quadrature rule used for the approximation of integrals over the s-dimensional unit cube. Every lattice rule may be characterised by an integer r called the rank of the rule and a set of r positive integers called the invariants. By exploiting the group-theoretic structure of lattice rules we determine the number of distinct lattice rules having given invariants. Some numerical results supporting the theoretical results are included. These numerical results are obtained by calculating the Smith normal form of certain integer matrices.

Sign in / Sign up

Export Citation Format

Share Document