An iterative algorithm for searching a scaling matrix for diagonal dominance

Diagonal dominance of matrices and M-matrices (and H-matrices) play an important role in stability theory of dynamical systems. But it is difficult to determine the scaling matrix G = diag(g1, …, gn) (g1, …, gn > 0) with AG being a strictly diagonally dominant matrix. In this paper, an convergent iterative algorithm for determine the scaling matrix for an irreducible M-matrix (H-matrix) A is presented.