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In this paper, we establish some conditions for the existence and the representations for the common ( P, Q) generalized reflexive and anti-reflexive solutions of matrix equations $$AX=B$$ and $$XC=D$$ , where P and Q are two generalized reflection matrices. Moreover, in corresponding solution set of the equations, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm has been presented. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new conditions for the existence and the representations for the $$(P, Q)$$ generalized reflexive and anti-reflexive solutions to matrix equation $$AX = B$$ with respect to the generalized reflection matrix dual $$(P, Q)$$ . Moreover, in corresponding solution sets of the equation, the explicit expressions of the nearest matrix to a given matrix in the Frobenius norm have been provided. [ABSTRACT FROM AUTHOR]

A fast algorithm is proposed for numerically computing an interval matrix containing the minimal nonnegative solution to the nonsymmetric T-Riccati equation. The cost of this algorithm is cubic plus that for numerically solving the equation. The algorithm proves that the solution contained in the interval matrix is unique and equal to the minimal nonnegative solution. Numerical results show the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

We consider the problem of solving a rational matrix equation arising in the solution of G-networks. We propose and analyze two numerical methods: a fixed point iteration and the Newton-Raphson method. The fixed point iteration is shown to be globally convergent with linear convergence rate, while the Newton method is shown to have a local convergence, with quadratic convergence rate. Numerical experiments show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The operator defined by the left-hand side of the matrix equation is not linear in the space of complex matrices $$X$$ . However, it becomes a linear operator if every matrix $$X$$ is replaced by the pair of real matrices of the same size, namely, by its real and imaginary parts. Introducing an appropriate scalar product in the resulting real space, we find necessary and sufficient conditions for this operator to be normal. [ABSTRACT FROM AUTHOR]