Note to the Global GMRES for Solving the Matrix Equation AXB = F
نویسنده
چکیده
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 called as the extended Gl-GMRES (EGlGMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method. Keywords—Matrix equation, Iterative method, linear systems, block Krylov subspace method, global generalized minimum residual (Gl-GMRES).
منابع مشابه
Convergence 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 کاملTheoretical 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 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 کاملPreconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation
Introduction Fractional differential equations (FDEs) have attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme may be a good approach, particularly, the schemes in numerical linear algebra for solving ...
متن کاملGlobal R-linear GMRES for solving a class of R-linear matrix equations
We present a new minimal residual method, called global R-linear GMRES, to solve the R-linear matrix equations X + AXB = C and X + AXB = C, where C, X ∈ Cm×n, X denotes the complex conjugate of X, X its complex conjugate transpose, and A, B are complex matrices with appropriate dimensions. We show that the new method requires fewer matrix-matrix products than the global GMRES method applied to ...
متن کامل