TY - JOUR
T1 - Minimization Problem for Symmetric Orthogonal Anti-Symmetric Matrices
AU - Yuan Lei, Anping Liao & Lei Zhang
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, Generalized singular value decomposition, Canonical correlation decomposition.
AB - <p style="text-align: justify;">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.</p>