BLOCKWISE MATRIX MULTI-SPLITTING MULTIPARAMETER BLOCK RELAXATION METHODS

In this paper, a class of parallel blockwise matrix multisplitting blo ck relaxation methods, including the blockwise matrix multisplitting b lock symmetric accelerated overrelaxation method, the blockwise matrix multisplitting block unsymmetric and symmetric successive overrelaxat ion methods and the blockwise matrix multisplitting block unsymmetric and symmetric Gauss-Seidel methods, etc., is established for the large sparse block system of linear equations, and its convergence theory i s set up thorouthly when the coefficient matrix is a block H-matrix. A lso, the new methods are further extended by relaxing different block elements of the iterations with different relaxation parameters and, t herefore, general frameworks of parallel blockwise matrix multisplitti ng block relaxation methods for solving the block system of linear equ ations are naturally obtained.