On the Convergence of Iterative Methods for Semidefinite Linear Systems

Abstract

Necessary and sufficient conditions for the energy norm convergence of the classical iterative methods for semidefinite linear systems are obtained in this paper. These new conditions generalize the classic notion of the P‐regularity introduced by Keller [J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 2 (1965), pp. 281–290].