Least squares (P,Q)-orthogonal symmetric solutions of the matrix equation and its optimal approximation

Ela Least Squares (p,q)-orthogonal Symmetric Solutions of the Matrix Equation and Its Optimal Approximation∗

In this paper, the relationship between the (P,Q)-orthogonal symmetric and symmetric matrices is derived. By applying the generalized singular value decomposition, the general expression of the least square (P,Q)-orthogonal symmetric solutions for the matrix equation AXB = C is provided. Based on the projection theorem in inner space, and by using the canonical correlation decomposition, an ana...

Least-Squares Solutions of the Matrix Equation AXA= B Over Bisymmetric Matrices and its Optimal Approximation

A real n × n symmetric matrix X = (x i j)n×n is called a bisymmetric matrix if x i j = xn+1− j,n+1−i . Based on the projection theorem, the canonical correlation decomposition and the generalized singular value decomposition, a method useful for finding the least-squares solutions of the matrix equation AXA= B over bisymmetric matrices is proposed. The expression of the least-squares solutions ...

Minimization Problem for Symmetric Orthogonal Anti - Symmetric Matrices

By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution b X, which is both a least-squares symmetric orthogonal anti-symmetric solution of the matrix equation A XA = B and a best approximation to a given matrix X∗. Moreover, a numerical algorithm for finding this o...

Global least squares solution of matrix equation $sum_{j=1}^s A_jX_jB_j = E$

In this paper, an iterative method is proposed for solving matrix equation $sum_{j=1}^s A_jX_jB_j = E$. This method is based on the global least squares (GL-LSQR) method for solving the linear system of equations with the multiple right hand sides. For applying the GL-LSQR algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are dened. It is p...

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