scholarly journals Randomized Polynomial Lattice Rules for Multivariate Integration and Simulation

2003 ◽  
Vol 24 (5) ◽  
pp. 1768-1789 ◽  
Author(s):  
Christiane Lemieux ◽  
Pierre L'Ecuyer
Keyword(s):  
Lattice Rules ◽  
Multivariate Integration

scholarly journals Construction algorithms for polynomial lattice rules for multivariate integration

2005 ◽  
Vol 74 (252) ◽  
pp. 1895-1922 ◽  
Author(s):  
J. Dick ◽  
F. Y. Kuo ◽  
F. Pillichshammer ◽  
I. H. Sloan
Keyword(s):  
Lattice Rules ◽  
Multivariate Integration ◽  
Construction Algorithms

scholarly journals Constructing Embedded Lattice Rules for Multivariate Integration

2006 ◽  
Vol 28 (6) ◽  
pp. 2162-2188 ◽  
Author(s):  
Ronald Cools ◽  
Frances Y. Kuo ◽  
Dirk Nuyens
Keyword(s):  
Lattice Rules ◽  
Multivariate Integration

The Strong Tractability of Multivariate Integration Using Lattice Rules

2004 ◽  
pp. 259-273 ◽  
Author(s):  
Fred J. Hickernell ◽  
Ian H. Sloan ◽  
Grzegorz W. Wasilkowski
Keyword(s):  
Lattice Rules ◽  
Multivariate Integration

scholarly journals Constructions of general polynomial lattices for multivariate integration

2007 ◽  
Vol 76 (1) ◽  
pp. 93-110 ◽  
Author(s):  
Peter Kritzer ◽  
Friedrich Pillichshammer
Keyword(s):  
Hilbert Spaces ◽  
Lattice Rules ◽  
Irreducible Polynomials ◽  
Worst Case ◽  
Multivariate Integration ◽  
Construction Algorithm ◽  
General Polynomial ◽  
Construction Algorithms ◽  
Digital Nets

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 moduloarbitrarypolynomials.

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.

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
Sign in / Sign up

Export Citation Format

Share Document