Volume 25, Issue 5
Optimal Approximate Solution of the Matrix Equation AXB=C Over Symmetric Matrices
DOI:

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

15A24 65F20 65F22 65K10.

@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 KW - Optimal approximate solution KW - Generalized singular value decomposition KW - 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.