The Conditions for the Convergence of Power Scaled Matrices and Applications

Abstract

For an invertible diagonal matrix D , the convergence of the power scaled matrix sequence N N D A  is investigated. As a special case, necessary and sufficient conditions are given for the convergence of NN D T  , where T is triangular. These conditions involve both the spectrum as well as the diagraph of the matrix T . The results are then used to privide a new proof for the convergence of subspace iteration.