full
search.png

Search

close.png

Cancel

arrow
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

Preview Full PDF 1983 19279

Cited by

google scholar semantic scholar
Export citation
  • 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.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JCM-21-175, author = {}, 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 $X$ 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 & Zhongzhi Bai. (1970). Least-Squares Solution of $AXB = D$ over Symmetric Positive Semidefinite Matrices $X$. Journal of Computational Mathematics. 21 (2). 175-182. doi:
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard