Blockwise matrix multi-splitting multi-parameter block relaxation methods*

Abstract

In this paper, a class of parallel blockwise matrix multisplitting block relaxation methods, including the blockwise matrix multisplitting block symmetric accelerated overrelaxation method, the blockwise matrix multisplitting block unsymmetric and symmetric successive overrelaxation 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 is set up thorouthly when the coefficient matrix is a block H-matrix. Also, the new methods are further extended by relaxing different block elements of the iterations with different relaxation parameters and, therefore, general frameworks of parallel blockwise matrix multisplitting block relaxation methods for solving the block system of linear equations are naturally obtained.