Abstract
In this paper, we investigate a variant of the restarted GMRES method for solving a series of large sparse linear systems. Restarting is carried out by augmenting Krylov subspaces with some recently generated error approximations from the seed system. The method can preserve a nice property that allows solving the seed and the added linear systems at the cost of only one matrix–vector multiplication per iteration. Compared with solving each added linear system separately, the advantage of the new scheme is to lower down the overall cost of solving all added linear systems. Numerical experiments illustrate the efficiency of the acceleration strategy.
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