In this paper, we propose two iterative algorithms for finding the Hermitian reflexive and
skew-Hermitian solutions of the Sylvester matrix equation AX+ XB= C, respectively. We …

Purpose–The purpose of this paper is to find the efficient iterative methods for solving the
general matrix equation A1X+ XA2+ A3XH+ XHA4= B (including Lyapunov and Sylvester …

Let R 2 C m× m and S Î C n× n be nontrivial involution matrices, ie, R= R− 1 6 ¹±I and S= S-1
¹±I. An m× n complex matrix A is said to be an (R, S)-symmetric ((R, S)-skew symmetric) …

Closed form solutions to a family of generalized Sylvester matrix equation in form of∑ i=
0ϕAiXFi+∑ i= 0ψBkYFk=∑ j= 0φEjRFj are given by using the so-called Kronecker matrix …

Solving linear matrix equations has various applications in control theory, in engineering, in
scientific computations and various other fields. By applying generalization of the Hermitian …

It is known that solving coupled matrix equations with complex matrices can be very difficult
and it is sufficiently complicated. In this work, we propose two iterative algorithms based on …

In this paper, an iterative algorithm is established for finding the generalized bisymmetric
solution group to the coupled matrix equations (including the generalized (coupled) …

Let R∈ Cm× m and S∈ Cn× n be nontrivial involution matrices; ie R= R− 1≠±I and S= S−
1≠±I. An m× n complex matrix A is said to be a (R, S)-symmetric ((R, S)-skew symmetric) …

An n× n real matrix P is said to be a symmetric orthogonal matrix if P= P− 1= PT. An n× n real
matrix X is called a generalized centro-symmetric matrix with respect to P, if X= PXP. It is …

In this paper, we propose a new algorithm to solve the Sylvester matrix equation XA+ BX= C.
The technique consists of orthogonal reduction of the matrix A to a block upper Hessenberg …