Block CMRH method for solving matrix equations

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 [1, 2]. On dense matrices, the CMRH method is less expensive and requires less storage than other Krylov methods. In this paper, we present the block CMRH method for solving nonsymmetric linear systems with multiple right hand sides. This method is based on the block Hessenberg process. Finally, some numerical examples are given to illustrate the effectiveness of the presented method.