By extending the idea of LSMR method, we present an iterative method to solve the general coupled matrix equations , , (including the generalized (coupled) Lyapunov and Sylvester matrix equations as special cases) over some constrained matrix groups...

In this paper, some necessary and sufficient conditions are established for the existence of solutions to the system of operator equations $BXA=B=AXB$ in the setting of bounded linear operators on a Hilbert space, where ...

This paper presents a new version of the successive approximations method for solving Sylvester equations AX − XB = C, where A and B are symmetric negative and positive definite matrices, respectively. This method is based ...

We investigate positive definite solutions of nonlinear matrix equations $X-f(\\Phi(X))=Q$ and $X-\\sum_{i=1}^{m}f(\\Phi_i(X))=Q$, where $Q$ is a positive definite matrix, $\\Phi$ and $\\Phi_i ~~(1\\leq i\\leq m)$ are positive linear maps...

‎In this paper‎, ‎we first investigate the matrix equation $ AXB+CYD=G $‎, ‎where $ A‎, ‎B‎, ‎C‎, ‎D $ and $ G $ are arbitrary matrices in a new fashion‎. ‎Then‎, ‎we establish some necessary and sufficient conditions for the existence of a solution...

This paper presents preconditioned Galerkin and minimal residual algorithms for the solution of Sylvester equations AX−XB=C. Given two good preconditioner matrices M and N for matrices A and B, respectively, we solve the ...

CMRH method (Changing minimal residual with Hessenberg process) is an iterative

method for solving nonsymmetric linear systems. This method is similar to QMR method

but based on the Hessenberg process instead ...

In this paper, we present a nested splitting conjugate gradient (NSCG) iteration method for

solving a class of matrix equations with nonsymmetric coefficient matrices. This method is

actually inner/outer iterations, which employs a CG...

and Chebyshev spectral differentiationmatrix to solve numerically a class of initial-boundary value problems of the time fractional Fokker-Planck equation on a finite domain. The presentedmethod reduces themain problem to a generalized Sylvester matrix equation...