The anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximation
Given the linear matrix equation \(A^T XA = B\), by using the generalized singular value decomposition, this paper deals with (1) the necessary and sufficient conditions for the existence of the anti-symmetric ortho-symmetric solution \(X\), and (2) the existence and uniqueness of its optimal approximation \(X^*\) satisfying \(\min_X \| X - X^*\| \). Finally, numerical methods of the optimal approximation are formulated and illustrative numerical experiments are presented.
scientific article; zbMATH DE number 5354630
scientific article