ON THE CONVERGENCE OF THE PARALLEL MULTISPLITTING AOR ALGORITHM

We present a class of relaxed parallel multisplitting algorithms, called the parallel multisplitting AOR algorithm, for solving large nonsingular systems of equations Ax = b. This new algorithm is a generalization and improvement of the relaxed parallel multisplitting method [Linear Algebra Appl. 119:141-152 (1989)]. Based on the new algorithm model, we establish another algorithm called the relaxed parallel multisplitting AOR algorithm. The convergence of these algorithms is discussed; under the condition that A is a monotone matrix, we obtain corresponding convergence results. These convergence conditions are convenient to verify.