Convergence of relaxed parallel multisplitting methods
\textit{D. P. O'Leary} and \textit{R. E. White} [SIAM J. Algebraic Discrete Methods 6, 630-640 (1985; Zbl 0582.65018)] introduced, for large sparse systems \(Ax=b\), parallel iterative methods based on several splittings of A. They also introduce a positive relaxation parameter \(\omega\) in the same way as in the relaxed Jacobi method; it may also be introduced as in the Gauss-Seidel method. In the present paper it is proved that, if A is an H-matrix, these methods converge if \(\omega \in (0,\omega_ 0)\) with \(\omega_ 0>1\).
scientific article; zbMATH DE number 4108012
scientific article