Mr. Smith goes to Las Vegas: Randomized parallel computation of the Smith Normal form of polynomial matrices

1989 ◽  
pp. 317-322 ◽  
Author(s):  
Erich Kaltofen ◽  
M. S. Krishnamoorthy ◽  
B. David Saunders
Keyword(s):  
Normal Form ◽  
Parallel Computation ◽  
Las Vegas ◽  
Smith Normal Form ◽  
Polynomial Matrices

Multiplicativity of the Smith Normal Form

1994 ◽  
Vol 36 (3) ◽  
pp. 223-224 ◽  
Author(s):  
Morris Newman
Keyword(s):  
Normal Form ◽  
Smith Normal Form

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