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

Abstract

CMRH method (Changing minimal residual with Hessenberg process) is an iterative<br><br>method for solving nonsymmetric linear systems. This method is similar to QMR method<br><br>but based on the Hessenberg process instead of the Lanczos process. On dense matrices,<br><br>the CMRH method is less expensive and requires less storage than other Krylov methods.<br><br>This paper presents a block version of the CMRH algorithm for solving linear systems with<br><br>multiple right-hand sides. The new algorithm is based on the block Hessenberg process<br><br>and the iterates are characterized by a block version of the quasi-minimization property.<br><br>We analyze its main properties and show that under the condition of full rank of block<br><br>residual the block CMRH method cannot break down. Finally, some numerical examples<br><br>are presented to show the efficiency of the new method in comparison with the traditional<br><br>CMRH method and a comparison with the block GMRES method is also provided.<br><br>© 2018 Elsevier B.V.