Solutions to matrix equations X−AXB=CY+R and X−AX̂B=CY+R

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...

Non-trivial solutions to certain matrix equations

The existence of non-trivial solutions X to matrix equations of the form F (X,A1,A2, · · · ,As) = G(X,A1,A2, · · · ,As) over the real numbers is investigated. Here F and G denote monomials in the (n × n)-matrix X = (xij) of variables together with (n × n)-matrices A1,A2, · · · ,As for s ≥ 1 and n ≥ 2 such that F and G have different total positive degrees in X. An example with s = 1 is given by...

Approximate solutions to large Stein matrix equations

In the present paper, we propose numerical methods for solving the Stein equation AXC − X − D = 0 where the matrix A is large and sparse. Such problems appear in discrete-time control problems, filtering and image restoration. We consider the case where the matrix D is of full rank and the case where D is factored as a product of two matrices. The proposed methods are Krylov subspace methods ba...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

Efficient Solutions of Coupled Matrix and Matrix Differential Equations

In Kronecker products works, matrices are some times regarded as vectors and vectors are some times made in to matrices. To be precise about these reshaping we use the vector and diagonal extraction operators. In the present paper, the results are organized in the following ways. First, we formulate the coupled matrix linear least-squares problem and present the efficient solutions of this prob...