(untitled) (Journal of Computational Mathematics, 2007)
By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution 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.