‎The global generalized minimum residual (Gl-GMRES)‎ ‎method is examined for solving the generalized Sylvester matrix equation‎ ‎[sumlimits_{i = 1}^q {A_i } XB_i = C.]‎ ‎Some new theoretical results are elaborated for‎ ‎the proposed method by employing the Schur complement‎. ‎These results can be exploited to establish new convergence properties‎ ‎of the Gl-GMRES method for solving genera...

‎the global generalized minimum residual (gl-gmres)‎ ‎method is examined for solving the generalized sylvester matrix equation‎ ‎[sumlimits_{i = 1}^q {a_i } xb_i = c.]‎ ‎some new theoretical results are elaborated for‎ ‎the proposed method by employing the schur complement‎. ‎these results can be exploited to establish new convergence properties‎ ‎of the gl-gmres method for solving genera...

In this paper‎, ‎we study convergence behavior of the global FOM (Gl-FOM) and global GMRES (Gl-GMRES) methods for solving the matrix equation $AXB=C$ where $A$ and $B$ are symmetric positive definite (SPD)‎. ‎We present some new theoretical results of these methods such as computable exact expressions and upper bounds for the norm of the error and residual‎. ‎In particular‎, ‎the obtained upper...

‎the global fom and gmres algorithms are among the effective‎ ‎methods to solve sylvester matrix equations‎. ‎in this paper‎, ‎we‎ ‎study these algorithms in the case that the coefficient matrices‎ ‎are real symmetric (real symmetric positive definite) and extract‎ ‎two cg-type algorithms for solving generalized sylvester matrix‎ ‎equations‎. ‎the proposed methods are iterative projection metho...

in this paper‎, ‎we study convergence behavior of the global fom (gl-fom) and global gmres (gl-gmres) methods for solving the matrix equation $axb=c$ where $a$ and $b$ are symmetric positive definite (spd)‎. ‎we present some new theoretical results of these methods such as computable exact expressions and upper bounds for the norm of the error and residual‎. ‎in particular‎, ‎the obtained upper...

The solution of large scale Sylvester matrix equation plays an important role in control and large scientific computations. A popular approach is to use the global GMRES algorithm. In this work, we first consider the global GMRES algorithm with weighting strategy, and propose some new schemes based on residual to update the weighting matrix. Due to the growth of memory requirements and computat...

In this paper, we propose two new algorithms based on modified global Arnoldi algorithm for solving large Sylvester matrix equations AX + XB = C where A ∈ Rn×n, B ∈ Rs×s, X and C ∈ Rn×s. These algorithms are based on the global FOM and GMRES algorithms and we call them by Global FOM-SylvesterLike(GFSL) and Global GMRES-Sylvester-Like(GGSL) algorithms, respectively. Some theoretical results and ...

Restarted GMRES is one of the most popular methods for solving large nonsymmetric linear systems. The algorithm GMRES(m) restarts every m iterations. It is generally thought the information of previous GMRES cycles is lost at the time of a restart, so that each cycle contributes to the global convergence individually. However, this is not the full story. In this paper, we shed light on the rela...

‎The global FOM and GMRES algorithms are among the effective‎ ‎methods to solve Sylvester matrix equations‎. ‎In this paper‎, ‎we‎ ‎study these algorithms in the case that the coefficient matrices‎ ‎are real symmetric (real symmetric positive definite) and extract‎ ‎two CG-type algorithms for solving generalized Sylvester matrix‎ ‎equations‎. ‎The proposed methods are iterative projection metho...

In the present work, we propose a new projection method for solving the matrix equation AXB = F . For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be calle...