论文标题
超零散的TODA晶格和史密斯的biDiagonal矩阵正常形式
The ultradiscrete Toda lattice and the Smith normal form of bidiagonal matrices
论文作者
论文摘要
离散的TODA晶格保留了三角矩阵的特征值，并且可以在适当的条件下证明依赖变量与特征值的收敛。我们表明，超级进出的TODA晶格可以保留特定比尼测基质在主要理想域上的不变因子，并证明使用盒子和球系统的属性，依赖变量会收敛到不变因子。使用这个事实，我们提出了一种计算给定矩阵的史密斯法线形式的新方法。
The discrete Toda lattice preserves the eigenvalues of tridiagonal matrices, and convergence of dependent variables to the eigenvalues can be proved under appropriate conditions. We show that the ultradiscrete Toda lattice preserves invariant factors of a certain bidiagonal matrix over a principal ideal domain, and prove convergence of dependent variables to invariant factors using properties of box and ball system. Using this fact, we present a new method for computing the Smith normal form of a given matrix.
