On parallel multisplitting iterative methods for singular linear systems
The author considers the semiconvergence [cf. \textit{J. P. Kavanagh} and \textit{M. Neumann}, SIAM J. Matrix Anal. Appl. 10, 210--218 (1989; Zbl 0676.65025)] of parallel multisplitting iterative methods [cf. \textit{D. P. O'Leary} and \textit{R. C. White}, SIAM J. Alg. Disc. Methods 6, 630--640 (1985; Zbl 0582.65018)] and extrapolated parallel methods [cf. \textit{A. Frommer} and \textit{G. Mayer}, Linear Algebra Appl. 119, 141--152 (1989; Zbl 0676.65022)] for finding solutions to singular solvable systems of linear equations. After some preliminary definitions and facts, three main cases: \(P\)-regular, sub-regular and nonnegative multisplittings are investigated. Related lemmas and theorems are stated and proved. The final section contains theorems concerning conditions for the semiconvergence of parallel generalized accelerated overrelaxation (GAOR), block AOR (BAOR), AOR, parallel generalized successive overrelaxation (GSOR), block SOR (BSOR), SOR, extrapolated parallel (generalized, block) AOR and extrapolated parallel (general, block) SOR methods which are simple conclusions for the results proved in previous sections.
parallel multisplitting iterative methods
scientific article; zbMATH DE number 2137707
scientific article