TY - JOUR
T1 - Least-Squares Solution of $AXB = D$ over Symmetric Positive Semidefinite Matrices $X$
AU - Anping Liao & Zhongzhi Bai
JO - Journal of Computational Mathematics
VL - 2
SP - 175
EP - 182
PY - 2003
DA - 2003/04
SN - 21
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/10270.html
KW - Least-squares solution, Matrix equation, Symmetric positive semidefinite matrix, Generalized singular value decomposition.
AB - <p style="text-align: justify;">Least-squares solution of $AXB = D$ with respect to symmetric positive semidefinite matrix $X$ is considered. By making use of the generalized singular value decomposition, we derive general analytic formulas, and present necessary and sufficient conditions for guaranteeing the existence of the solution. By applying MATLAB 5.2, we give some numerical examples to show the feasibility and accuracy of this construction technique in the finite precision arithmetic.</p>