Volume 25, Issue 2
Minimization Problem for Symmetric Orthogonal Anti-Symmetric Matrices
DOI:

J. Comp. Math., 25 (2007), pp. 211-220

Published online: 2007-04

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• Abstract

By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution $\widehat X$, which is both a least-squares symmetric orthogonal anti-symmetric solution of the matrix equation $A^TXA=B$ and a best approximation to a given matrix $X^*$. Moreover, a numerical algorithm for finding this optimal approximate solution is described in detail, and a numerical example is presented to show the validity of our algorithm.

• Keywords

Symmetric orthogonal anti-symmetric matrix Generalized singular value decomposition Canonical correlation decomposition

• AMS Subject Headings

@Article{JCM-25-211, author = {}, title = {Minimization Problem for Symmetric Orthogonal Anti-Symmetric Matrices}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {2}, pages = {211--220}, abstract = { By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution $\widehat X$, which is both a least-squares symmetric orthogonal anti-symmetric solution of the matrix equation $A^TXA=B$ and a best approximation to a given matrix $X^*$. Moreover, a numerical algorithm for finding this optimal approximate solution is described in detail, and a numerical example is presented to show the validity of our algorithm. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8686.html} }
TY - JOUR T1 - Minimization Problem for Symmetric Orthogonal Anti-Symmetric Matrices JO - Journal of Computational Mathematics VL - 2 SP - 211 EP - 220 PY - 2007 DA - 2007/04 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8686.html KW - Symmetric orthogonal anti-symmetric matrix KW - Generalized singular value decomposition KW - Canonical correlation decomposition AB - By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution $\widehat X$, which is both a least-squares symmetric orthogonal anti-symmetric solution of the matrix equation $A^TXA=B$ and a best approximation to a given matrix $X^*$. Moreover, a numerical algorithm for finding this optimal approximate solution is described in detail, and a numerical example is presented to show the validity of our algorithm.