ON NECESSARY CONDITIONS FOR CONVERGENCE OF STATIONARY ITERATIVE METHODS FOR HERMITIAN DEFINITE AND SEMIDEFINITE LINEAR SYSTEMS
Andreas Frommer, Daniel B. Szyld · 2013
In an earlier paper (SIAM J. Matrix Anal. Appl. vol. 30 (2008), 925{938) we gave sucient conditions in terms of an energy seminorm for the convergence of stationary iterations for solving singular linear systems whose coecient matrix is Hermitian and positive semidenite. In this paper we show in which cases these conditions are also necessary, and show that they are not necesary in others. We present similar results for the nonsingular case, thus providing some converse results for theorems on P -regular splittings.