Iterative Algorithms For M-matrix And Its ‖A～(-1)‖_∞

This paper provides iterative algorithms for M-Matrix.Diagonal dominance of matrices and M-matrices (and H-matrices) play an important role in stability theory of dynamical systems. But it is difficult todetermine the scaling matrix G = diag(g₁,g₂,---,g_n) (g₁,,--,g_n >0), with AGbeing a strictly diagonally dominant matrix. In Chapter 2, a convergent iterative algorithm for determines the scaling matrix for an irreducible M-matrix (H-matrix) A is presented.In Chapter 3, we provide an iterative algorithm for calculating || A^-1 ||_∞ forM-matrices. When A is a M-matrix, this algorithm determines a positive diagonal matrix D so that AD is a so-called equi-diagonally dominant matrix. Then|| A^-1 ||_∞ for M-matrices and H-matrices can be evaluated.