A polynomial preconditioner for the CMRH algorithm
Summary: Many large and sparse linear systems can be solved efficiently by restarted GMRES and CMRH methods [\textit{H. Sadok}, Numer. Algorithms 20, No.~4, 303--321 (1999; Zbl 0936.65031)]. The CMRH\((m)\) method is less expensive and requires slightly less storage than GMRES\((m)\). But like GMRES, the restarted CMRH method may not converge. In order to remedy this defect, this paper presents a polynomial preconditioner for CMRH-based algorithm. Numerical experiments are given to show that the polynomial preconditioner is quite simple and easily constructed and the preconditioned CMRH\((m)\) with the polynomial preconditioner has better performance than CMRH\((m)\).
scientific article; zbMATH DE number 5904902
scientific article