scholarly journals The ultradiscrete Toda lattice and the Smith normal form of bidiagonal matrices

2021 ◽  
Vol 62 (9) ◽  
pp. 092701
Author(s):  
Katsuki Kobayashi ◽  
Satoshi Tsujimoto
Keyword(s):  
Normal Form ◽  
Toda Lattice ◽  
Smith Normal Form

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.

scholarly journals On the structure of least common multiple matrices from some class of matrices

2018 ◽  
Vol 10 (1) ◽  
pp. 179-184
Author(s):  
A.M. Romaniv
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Smith Normal Form ◽  
Least Common Multiple ◽  
The Matrix ◽  
Singular Matrices ◽  
Class Of Matrices ◽  
Smith Normal Forms ◽  
Invertible Matrices ◽  
Principal Ideal Domains

For non-singular matrices with some restrictions, we establish the relationships between Smith normal forms and transforming matrices (a invertible matrices that transform the matrix to its Smith normal form) of two matrices with corresponding matrices of their least common right multiple over a commutative principal ideal domains. Thus, for such a class of matrices, given answer to the well-known task of M. Newman. Moreover, for such matrices, received a new method for finding their least common right multiple which is based on the search for its Smith normal form and transforming matrices.

Quasi-symmetric designs and the Smith Normal Form

1992 ◽  
Vol 2 (2) ◽  
pp. 189-206 ◽  
Author(s):  
A. Blokhuis ◽  
A. R. Calderbank
Keyword(s):  
Normal Form ◽  
Smith Normal Form ◽  
Symmetric Designs

Smith meets Smith: Smith normal form of Smith matrix

2011 ◽  
Vol 59 (5) ◽  
pp. 557-564 ◽  
Author(s):  
Pauliina Ilmonen ◽  
Pentti Haukkanen
Keyword(s):  
Normal Form ◽  
Smith Normal Form

Smith normal form of some distance matrices

2016 ◽  
Vol 65 (6) ◽  
pp. 1117-1130 ◽  
Author(s):  
Ravindra B. Bapat ◽  
Masoud Karimi
Keyword(s):  
Normal Form ◽  
Smith Normal Form ◽  
Distance Matrices
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