Accuracy improvement of the Block BiCGSTAB method for linear systems with multiple right-hand sides by group-wise updating technique

Abstract

The Block BiCGSTAB method is an efficient method for solving linear systems with multiple right-hand sides. However, when the number of right-hand sides is large, this method may not generate high accuracyapproximate solution due to an error in the computation of matrix-matrix multiplication. In this paper, in order to improve the accuracy of the approximate solution, the recursions of the Block BiCGSTAB method are reconstructed by using the group-wise updating technique. Moreover, the convergence property of the proposed method is also improved when the number of right-hand sides is large.