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Volume 21, Issue 2
Least-Squares Solution of $AXB = D$ over Symmetric Positive Semidefinite Matrices $X$

Anping Liao & Zhongzhi Bai

J. Comp. Math., 21 (2003), pp. 175-182.

Published online: 2003-04

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  • Abstract

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.

  • Keywords

Least-squares solution, Matrix equation, Symmetric positive semidefinite matrix, Generalized singular value decomposition.

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COPYRIGHT: © Global Science Press

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@Article{JCM-21-175, author = {Anping Liao and Zhongzhi Bai}, title = {Least-Squares Solution of $AXB = D$ over Symmetric Positive Semidefinite Matrices $X$}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {2}, pages = {175--182}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10270.html} }
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 -

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.

Anping Liao and Zhongzhi Bai. (2003). Least-Squares Solution of $AXB = D$ over Symmetric Positive Semidefinite Matrices $X$. Journal of Computational Mathematics. 21 (2). 175-182. doi:
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