On the semiconvergence of additive and multiplicative splitting iterations for singular linear systems

Keywords: Additive/multiplicative splitting iteration method Singular linear systems Hermitian matrix Semiconvergence a b s t r a c t In this paper, we investigate the additive, multiplicative and general splitting iteration methods for solving singular linear systems. When the coefficient matrix is Hermitian, the semiconvergence conditions are proposed, which generalize some results of Bai [Z.-Z. Bai, On the convergence of additive and multiplicative splitting iterations for systems of linear equations, J. Comput. Appl. Math. 154 (2003) 195–214] for the nonsingular linear systems to the singular systems.