روش تکراری تصویری متوالی برای حل سیستم معادلات خطی با ماتریس ضرایب مثبت معین متقارن ax=b successive projection iterative method for solving matrix equation ax=b.

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

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

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...

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...

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

Diagonal and Monomial Solutions of the Matrix Equation AXB=C

In this article, we consider the matrix equation $AXB=C$, where A, B, C are given matrices and give new necessary and sufficient conditions for the existence of the diagonal solutions and monomial solutions to this equation. We also present a general form of such solutions. Moreover, we consider the least squares problem $min_X |C-AXB |_F$ where $X$ is a diagonal or monomial matrix. The explici...