The block CMRH method for solving nonsymmetric linear systems with multiple right-hand sides

CMRH method (Changing minimal residual with Hessenberg process) is an iterative method for solving nonsymmetric linear systems. This method is similar to QMR method but based on the Hessenberg process instead of the Lanczos process. On dense matrices, the CMRH method is less expensive and requires less storage than other Krylov methods. This paper presents a block version of the CMRH algorithm for solving linear systems with multiple right-hand sides. The new algorithm is based on the block Hessenberg process and the iterates are characterized by a block version of the quasi-minimization property. We analyze its main properties and show that under the condition of full rank of block residual the block CMRH method cannot break down. Finally, some numerical examples are presented to show the efficiency of the new method in comparison with the traditional CMRH method and a comparison with the block GMRES method is also provided.