A block GCROT(m,k) method for linear systems with multiple right-hand sides

This study is mainly focused on iterative solution to multiple linear systems with several right-hand sides. For solving such systems efficiently, we explore a new block GCROT(m,k) (BGCROT(m,k)) method, which is derived by extending GCROT(m,k) method [Jason E. Hicken, David W. Zingg, A simplified and flexible variant of GCROT for solving nonsymmetric linear systems, SIAM J. Sci. Comput. 32 (2010) 1672-1694]. We analyze its main properties. It is shown that under the condition of full rank of block residual, the Frobenius norm of the block residual generated by the proposed method is always nonincreasing. Moreover, we also present its block flexible version, BFGCROT(m,k). Finally, numerical examples demonstrate that the BGCROT(m,k) method and its flexible variant can achieve a smoothed residual and can be more competitive than some other block solvers.