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In this paper, the influence of errors which arise in matrix multiplications on the accuracy of approximate solutions generated by the Block BiCGSTAB method is analyzed. In order to generate high accuracy solutions, a new Block Krylov subspace method is also proposed. Some numerical experiments illustrate that high accuracy solutions can be obtained by using the proposed method compared with the Block BiCGSTAB method.

Block BiCGGR: a new Block Krylov subspace method for computing high accuracy solutions