On parallel multisplitting iterative methods for singular linear systems

In this paper, the semiconvergence of parallel multisplitting iterative methods and extrapolated parallel methods for singular linear systems is discussed. Some sufficient conditions for semiconvergence are presented whenever the multisplittings are P-regular, sub-regular or nonnegative. As special cases the semiconvergence of parallel generalized AOR, block AOR, AOR, parallel generalized SOR, block SOR, SOR, extrapolated parallel (generalized, block) AOR and extrapolated parallel (generalized, block) SOR methods are proved.