THE BLOCK HESSENBERG PROCESS FOR MATRIX EQUATIONS

In the present paper, we first introduce a block variant of the Hessenberg process and discuss its properties. Then, we show how to apply the block Hessenberg process in order to solve linear systems with multiple right-hand sides. More precisely, we define the block CMRH method for solving linear systems that share the same coefficient matrix. We also show how to apply this process for solving discrete Sylvester matrix equations. Finally, numerical comparisons are provided in order to compare the proposed new algorithms with other existing methods. Key words. Block Krylov subspace methods, Hessenberg process, Arnoldi process, CMRH, GMRES, low-rank matrix equations. AMS subject classifications. 65F10, 65F30