A parallel algorithm for preconditioning large and sparse linear systems is proposed. Both structural and numerical dropping are used to construct a preconditioner with proper structure. The Balance method is used to solve the linear system involving such preconditioner in each iteration.
The algorithm can be used together with any iterative method (GMRES is used for the experiments in this paper). As shown by numerical experiments, this approach is quite robust and has attractive parallel performance. It has been successful in solving quickly, and accurately, some ill-conditioned systems, which proved to be difficult for other preconditioned iterative methods.
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