The discrete Toda lattice preserves the eigenvalues of tridiagonal matrices, and convergence dependent variables to can be proved under appropriate conditions. We show that ultradiscrete invariant factors a certain bidiagonal matrix over principal ideal domain prove using properties box ball system. Using this fact, we present new method for computing Smith normal form given matrix.

The article discusses the matrices of the 1 n A , m n A , m N A forms, whose inversions are: tridiagonal matrix 1  n A (n dimension of the matrix), banded matrix m n A  (m the half-width band of the matrix) or block-tridiagonal matrix m N A  (N=n x m – full dimension of the block matrix; m the dimension of the blocks) and their relationships with the covariance matrices of measurements with ...

Until 1991, the simulation of coupled systems, in which electrochemical reactions are coupled with homogeneous chemical reactions in such a way that at least some of the relevant partial differential transport equations (pdes) contain terms for more than one species, was considered hard. The reason is that many such reaction mechanisms lead to thin reaction layers [1], necessitating the use of ...

A well–known property of an irreducible singular M–matrix is that it has a generalized inverse which is non–negative, but this is not always true for any generalized inverse. The authors have characterized when the Moore–Penrose inverse of a symmetric, singular, irreducible and tridiagonal M–matrix is itself an M–matrix. We aim here at giving new explicit examples of infinite families of matric...

A real symmetric matrix of order n has a full set of orthogonal eigenvectors. The most used approach to compute the spectrum of such matrices reduces first the dense symmetric matrix into a symmetric structured one, i.e., either a tridiagonal matrix [2, 3] or a semiseparable matrix [4]. This step is accomplished in O(n) operations. Once the latter symmetric structured matrix is available, its s...

Abstract. It is proved that the eigenvalues of the Jacobi Tau method for the second derivative operator with Dirichlet boundary conditions are real, negative and distinct for a range of the Jacobi parameters. Special emphasis is placed on the symmetric case of the Gegenbauer Tau method where the range of parameters included in the theorems can be extended and characteristic polynomials given by...

The article addresses a regular splitting of tridiagonal matrices. The given tridiagonal matrix A is rst expanded to an equivalent matrix e A and then split as e A = B R for which B is block-diagonal and every eigenvalue of B R is zero, i.e., (M N) = 0. The optimal splitting technique is applicable to various algorithms that incorporate one-dimensional solves or their approximations. Examples c...

In this paper the definition of semiseparable matrices is investigated. Properties of the frequently used definition and the corresponding representation by generators are deduced. Corresponding to the class of tridiagonal matrices another definition of semisepar-able matrices is introduced preserving the nice properties dual to the class of tridiagonal matrices. Several theorems and properties...