(Anti‐)Hermitian Generalized (Anti‐)Hamiltonian Solution to a System of Matrix Equations
Juan Yu, Qing-Wen Wang, Chang-Zhou Dong · Mathematical Problems in Engineering · 2014
We mainly solve three problems. Firstly, by the decomposition of the (anti‐)Hermitian generalized (anti‐)Hamiltonian matrices, the necessary and sufficient conditions for the existence of and the expression for the (anti‐)Hermitian generalized (anti‐)Hamiltonian solutions to the system of matrix equations AX = B, XC = D are derived, respectively. Secondly, the optimal approximation solution is obtained, where K is the (anti‐)Hermitian generalized (anti‐)Hamiltonian solution set of the above system and is the given matrix. Thirdly, the least squares (anti‐)Hermitian generalized (anti‐)Hamiltonian solutions are considered. In addition, algorithms about computing the least squares (anti‐)Hermitian generalized (anti‐)Hamiltonian solution and the corresponding numerical examples are presented.