Global Hessenberg and CMRH methods for a class of complex matrix equations

In this paper, we study how to use Hessenberg-based methods to solve a class of complex matrix equations, which is a general form of many known equations. A generalized global Hessenberg process is presented to construct the basis of complex matrix space. This process requires less work and storage because the basis it uses has more zero components. Then global Hessenberg (Gl-Hess) and global CMRH (Gl-CMRH) methods are proposed, which can be directly realized by the original coefficient matrices. The convergence of the Gl-CMRH method is analyzed. Numerical experiments show the efficiency of the methods and compare them with existing methods.