global least squares solution of matrix equation $sum_{j=1}^s a_jx_jb_j = e$

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...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

GLOBAL TOTAL LEAST SQUARES Global Total Least Squares

A method for the construction of open approximate models from vector time series Preface PhD research is a largely open proces in which a stimulating environment plays a crucial role. I am indebted to several people and institutions that shaped such an environment for me during the years since April 1990. First and for all, I would like to thank my supervisor, Christiaan Heij. He set me on the ...

Two special kinds of least squares solutions for the quaternion matrix equation AXB+CXD=E

The least-square bisymmetric solution to a quaternion matrix equation with applications

In this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation XA=B to have the least-square bisymmetric solution and give the expression of such solution when the solvability conditions are met. Futhermore, we consider the maximal and minimal inertias of the least-square bisymmetric solution to this equation. As applications, we derive sufficient and necess...

Least-Squares Covariance Matrix Adjustment

We consider the problem of finding the smallest adjustment to a given symmetric n × n matrix, as measured by the Euclidean or Frobenius norm, so that it satisfies some given linear equalities and inequalities, and in addition is positive semidefinite. This least-squares covariance adjustment problem is a convex optimization problem, and can be efficiently solved using standard methods when the ...