Least-Squares Solution with the Minimum-Norm for the Matrix Equation A T XB+B T X T A = D and Its Applications

2007 ◽  
Vol 23 (2) ◽  
pp. 269-280 ◽  
Author(s):  
An-ping Liao ◽  
Yuan Lei ◽  
Xi-yan Hu
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Minimum Norm ◽  
Least Squares Solution ◽  
The Matrix

scholarly journals Least-squares solution with the minimum-norm for the matrix equation (AXB, GXH) = (C, D)

2005 ◽  
Vol 50 (3-4) ◽  
pp. 539-549 ◽  
Author(s):  
An-Ping Liao ◽  
Yuan Lei
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Minimum Norm ◽  
Least Squares Solution ◽  
The Matrix

scholarly journals A Hermitian least squares solution of the matrix equation AXB=C subject to inequality restrictions

2012 ◽  
Vol 64 (6) ◽  
pp. 1752-1760 ◽  
Author(s):  
Ying Li ◽  
Yan Gao ◽  
Wenbin Guo
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Least Squares Solution ◽  
Inequality Restrictions ◽  
The Matrix

scholarly journals Minimal properties of the Drazin-inverse solution of a matrix equation

Filomat ◽  
2014 ◽  
Vol 28 (2) ◽  
pp. 383-395
Author(s):  
Marko Miladinovic ◽  
Sladjana Miljkovic ◽  
Predrag Stanimirovic
Keyword(s):  
Least Squares ◽  
Minimization Problem ◽  
Matrix Equation ◽  
Inverse Solution ◽  
Drazin Inverse ◽  
Minimal Norm ◽  
Least Squares Solution ◽  
The Matrix

We present the Drazin-inverse solution of the matrix equation AXB = G as a least-squares solution of a specified minimization problem. Some important properties of the Moore-Penrose inverse are extended on the Drazin inverse by exploring the minimal norm properties of the Drazin-inverse solution of the matrix equation AXB = G. The least squares properties of the Drazin-inverse solution lead to new representations of the Drazin inverse of a given matrix, which are justified by illustrative examples.

An efficient method for special least squares solution of the complex matrix equation (AXB,CXD)=(E,F)

2018 ◽  
Vol 76 (8) ◽  
pp. 2001-2010 ◽  
Author(s):  
Fengxia Zhang ◽  
Musheng Wei ◽  
Ying Li ◽  
Jianli Zhao
Keyword(s):  
Least Squares ◽  
Efficient Method ◽  
Matrix Equation ◽  
Complex Matrix ◽  
Least Squares Solution

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

2010 ◽  
Vol 20 ◽  
Author(s):  
Lin-lin Zhao ◽  
Guo-linag Chen ◽  
Qing-bin Liu
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Optimal Approximation ◽  
The Matrix

Relations between least-squares and least-rank solutions of the matrix equation

2013 ◽  
Vol 219 (20) ◽  
pp. 10293-10301 ◽  
Author(s):  
Yongge Tian ◽  
Hongxing Wang
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
The Matrix

Least squares solutions of the matrix equation AXB+CYD=E with the least norm for symmetric arrowhead matrices

2014 ◽  
Vol 226 ◽  
pp. 719-724 ◽  
Author(s):  
Hongyi Li ◽  
Zongsheng Gao ◽  
Di Zhao
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
The Matrix
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