The generalized centro-symmetric and least squares generalized centro-symmetric solutions of the matrix equation AYB + CYTD = E

Abstract

An n×n real matrix P is said to be a symmetric orthogonal matrix if P = P −1 = P T . An n×n real matrix Y is called a generalized centro-symmetric with respect to P, if Y = PYP. It is obvious that every matrix is also a generalized centrosymmetric matrix with respect to I. In this work by extending the conjugate gradient approach, two iterative methods are proposed for solving the linear matrix equation

Solving coupled matrix equations over generalized bisymmetric matrices

“…Due to their wide applications, various authors presented several methods for solving the matrix equations in recent years [6][7][8][9][10][11][12][13][14][15][16][17][18]42]. For example, Dehghan and Hajarian [19][20][21][22][23][24][25][26] proposed several efficient iterative algorithms for solving Sylvester matrix equations. In [27], an efficient method was proposed to find the generalized bisymmetric solutions of the matrix equation In [28], Cramer's rules for some quaternion matrix equations were presented within the framework of the theory of the column and row determinants.…”

On the generalized reflexive and anti-reflexive solutions to a system of matrix equations

“…The HGI algorithms [16,21] and HLSI algorithms [20,21,18] for solving general (coupled) matrix equations are innovational and computationally efficient numerical methods and were proposed based on the hierarchical identification principle [17,19] which regards the unknown matrix as the system parameter matrix to be identified. In [15,[8][9][10][11][12], some efficient iterative methods were proposed to solve Sylvester and Lyapunov matrix equations. Zhou and Duan [43,44,46] established the solution of the several generalized Sylvester matrix equations.…”

An Iterative Algorithm for the Least Squares Solutions of Matrix Equations Over Symmetric Arrowhead Matrices

“…The idea of conjugate gradient (CG) method [33] has been developed for constructing iterative algorithms to compute the solutions of different kinds of linear matrix equations over generalized reflexive and anti-reflexive, generalized bisymmetric, generalized centro-symmetric, mirror-symmetric, skewsymmetric and (P, Q)-reflexive matrices, for more details see [2,7,8,9,16,22,29,38] and the references therein. For instance, Peng et al [28] have proposed an iterative algorithm for finding the bisymmetric solutions of matrix equation…”