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

iterative method for mirror-symmetric solution of matrix equation axb + cy d = e

Iterative Method for Mirror-symmetric Solution of Matrix Equation Axb + Cy D = E

Mirror-symmetric matrices have important applications in studying odd/even-mode decomposition of symmetric multiconductor transmission lines (MTL). In this paper, we propose an iterative algorithm to solve the mirror-symmetric solution of matrix equation AXB + CY D = E. With it, the solvability of the equation over mirror-symmetric X, Y can be determined automatically. When the equation is cons...

An Iterative Method for the Generalized Centro-symmetric Solution of a Linear Matrix Equation Axb + Cy D = E

A matrix P ∈ Rn×n is said to be a symmetric orthogonal matrix if P = P T = P−1. A matrix A ∈ Rn×n is said to be generalized centro-symmetric (generalized central anti-symmetric )with respect to P , if A = PAP (A = −PAP ). In this paper, an iterative method is constructed to solve the generalized centrosymmetric solutions of a linear matrix equation AXB + CY D = E, with real pair matrices X and ...

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

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...

An efficient iterative method for solving the matrix equation AXB + CYD = E

Ranks and Independence of Solutions of the Matrix Equation Axb + Cy D = M

Suppose AXB + CY D = M is a consistent matrix equation. In this paper, we give some formulas for the maximal and minimal ranks of two solutions X and Y to the equation. In addition, we investigate the independence of solutions X and Y to this equation.