Symbolic computations of the solution of simultaneous equation, the determinant and the eigen polynomial of a large scaled sparse matrix in terms of the discrete Toda equation(Applied Integrable Systems, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Abstract

A new method for constructing the minimum polynomial for the symbolic computation in terms of the discrete Toda equation is proposed. For the sparse matrices, the proposed method is efficiently carried out on a finite field arithmetic avoiding the division by zero. As a consequence, this paper presents new methods for the symbolic computation of the solution of simultaneous equation, the determinant and the eigen polynomial of a large scaled sparse matrix.