Alireza Ataei

In this thesis, we introduce Sylvester equation and then to solve it, we introduce a four-parameter version of the GMHSS iterative method. Under suitable conditions, we check the convergence of the GMHSS iterative method and state an upper bound for the spectral radius of the iterative matrix of this method and present the optimal parameters that minimize this upper bound. In order to improve the efficiency(saving a lot of calcu- lations of the iterative GMHSS method), the imprecise version of the iterative GMHSS method(IGMHSS) is presented. At the end, we present some numerical tests to confirm the efficiency of the GMHSS iterative method, and the results are compared with the re- sults of the HSS and MHSS iterative methods. In addition, we present a numerical com- parison of the GMHSS iterative method with the inexact version of the iterative method GMHSS(IGMHSS). Numerical results show that the iterative process of the IGMHSS in terms of time is a better method than the iterative process of GMHSS to solve Sylvester equation.