Semiconvergence of P-regular splittings for solving singular linear systems

We investigate necessary and sufficient conditions for semiconvergence of a splitting for solving singular linear systems, where the coefficient matrix A is a singular EP matrix. When A is a singular Hermitian matrix, necessary and sufficient conditions for semiconvergence of P-regular splittings are given, which generalize known results. As applications, the necessary and sufficient conditions for semiconvergence of block AOR and SSOR iterative methods are derived. A numerical example is given to illustrate the theoretical results. The work is supported by the National Natural Science Foundation of China under grant 10371056, the Foundation for the Authors of the National Excellent Doctoral Thesis Award of China under grant 200720 and the Natural Science Foundation of Jiangsu Province of China under grant BK2006725.