Weighted Versions of Gl-fom and Gl-gmres for Solving General Coupled Linear Matrix Equations
نویسندگان
چکیده
More recently, Beik and Salkuyeh [F. P. A. Beik and D. K. Salkuyeh, On the global Krylov subspace methods for solving general coupled matrix equations, Computers and Mathematics with Applications, 62 (2011) 4605–4613] have presented the Gl-FOM and Gl-GMRES algorithms for solving the general coupled linear matrix equations. In this paper, two new algorithms called weighted Gl-FOM (WGl-FOM) and weighted Gl-GMRES (WGl-GMRES) are proposed for solving the general coupled linear matrix equations. In order to accelerate the speed of convergence, a new inner product is used. Invoking the new inner product and a new matrix product, the weighted global Arnoldi algorithm is introduced which will be utilized for employing the WGlFOM and WGl-GMRES algorithms to solve the linear coupled linear matrix equations. After introducing the weighted methods, some relations that link Gl-FOM (Gl-GMRES) to its weighted version are established. Numerical experiments are presented to illustrate the effectiveness of the new algorithms in comparison with Gl-FOM and Gl-GMRES for solving the linear coupled linear matrix equations.
منابع مشابه
Theoretical results on the global GMRES method for solving generalized Sylvester matrix equations
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...
متن کاملConvergence analysis of the global FOM and GMRES methods for solving matrix equations $AXB=C$ with SPD coefficients
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...
متن کاملOn the global Krylov subspace methods for solving general coupled matrix equations
In the present paper, we propose the global full orthogonalization method (Gl-FOM) and global generalized minimum residual (Gl-GMRES) method for solving large and sparse general coupled matrix equations
متن کاملNew variants of the global Krylov type methods for linear systems with multiple right-hand sides arising in elliptic PDEs
In this paper, we present new variants of global bi-conjugate gradient (Gl-BiCG) and global bi-conjugate residual (Gl-BiCR) methods for solving nonsymmetric linear systems with multiple right-hand sides. These methods are based on global oblique projections of the initial residual onto a matrix Krylov subspace. It is shown that these new algorithms converge faster and more smoothly than the Gl-...
متن کاملGlobal conjugate gradient method for solving large general Sylvester matrix equation
In this paper, an iterative method is proposed for solving large general Sylvester matrix equation $AXB+CXD = E$, where $A in R^{ntimes n}$ , $C in R^{ntimes n}$ , $B in R^{stimes s}$ and $D in R^{stimes s}$ are given matrices and $X in R^{stimes s}$ is the unknown matrix. We present a global conjugate gradient (GL-CG) algo- rithm for solving linear system of equations with multiple right-han...
متن کامل