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Volume 25, Issue 5
Optimal Approximate Solution of the Matrix Equation $AXB=C$ over Symmetric Matrices

An-Ping Liao & Yuan Lei

J. Comp. Math., 25 (2007), pp. 543-552.

Published online: 2007-10

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  • Abstract

Let $S_E$ denote the least-squares symmetric solution set of the matrix equation $AXB=C$, where $A$, $B$ and $C$ are given matrices of suitable size. To find the optimal approximate solution in the set $S_E$ to a given matrix, we give a new feasible method based on the projection theorem, the generalized SVD and the canonical correction decomposition.

  • Keywords

Least-squares solution, Optimal approximate solution, Generalized singular value decomposition, Canonical correlation decomposition.

  • AMS Subject Headings

15A24, 65F20, 65F22, 65K10.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-543, author = {An-Ping Liao and Yuan Lei}, title = {Optimal Approximate Solution of the Matrix Equation $AXB=C$ over Symmetric Matrices}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {5}, pages = {543--552}, abstract = {

Let $S_E$ denote the least-squares symmetric solution set of the matrix equation $AXB=C$, where $A$, $B$ and $C$ are given matrices of suitable size. To find the optimal approximate solution in the set $S_E$ to a given matrix, we give a new feasible method based on the projection theorem, the generalized SVD and the canonical correction decomposition.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10347.html} }
TY - JOUR T1 - Optimal Approximate Solution of the Matrix Equation $AXB=C$ over Symmetric Matrices AU - An-Ping Liao & Yuan Lei JO - Journal of Computational Mathematics VL - 5 SP - 543 EP - 552 PY - 2007 DA - 2007/10 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10347.html KW - Least-squares solution, Optimal approximate solution, Generalized singular value decomposition, Canonical correlation decomposition. AB -

Let $S_E$ denote the least-squares symmetric solution set of the matrix equation $AXB=C$, where $A$, $B$ and $C$ are given matrices of suitable size. To find the optimal approximate solution in the set $S_E$ to a given matrix, we give a new feasible method based on the projection theorem, the generalized SVD and the canonical correction decomposition.

An-Ping Liao and Yuan Lei. (2007). Optimal Approximate Solution of the Matrix Equation $AXB=C$ over Symmetric Matrices. Journal of Computational Mathematics. 25 (5). 543-552. doi:
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