Weak-convergence of the splitting methods for solving singular systems is discussed. Two new concepts, k-order quasi-nonnegative splitting and k-order weak-convergence, are introduced. The equivalence conditions, asymptotic and monotone convergence, and comparison theorems are investigated for the k-order quasi-nonnegative splittings.
1 Subsidized by The Special Funds For Major State Basic Research Projects G1999032803, P.R. China. Permanent Address: Nantong Institute of Technology, Nantong 226007, Jiangsu Province, P.R. China.
2 Joint work with Zhong-Zhi BAI and Jin-Yun YUAN.