Iterative solutions to the linear matrix equation AXB + CXTD = E

Iterative Method for Mirror-Symmetric Solution of Matrix Equation AXB + CY D = E

A new Approximation to the solution of the linear matrix equation AXB = C

It is well-known that the matrix equations play a significant role in several applications in science and engineering. There are various approaches either direct methods or iterative methods to evaluate the solution of these equations. In this research article, the homotopy perturbation method (HPM) will employ to deduce the approximated solution of the linear matrix equation in the form AXB=C....

Iterative solutions to the linear matrix equation

In this paper the gradient based iterative algorithm is presented to solve the linear matrix equation AXB +CXD = E, where X is unknown matrix, A,B,C,D,E are the given constant matrices. It is proved that if the equation has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. Two numerical examples show that the introduced iterative a...

‎Finite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices

A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$‎. ‎An $ntimes n$‎ ‎complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$)‎. ‎In this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...

Iterative Solutions to Some Linear Matrix Equations

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F ; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = X ; (d) AXB+CY D = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be ob...