(Anti-)Hermitian Generalized (Anti-)Hamiltonian Solution to a System of Matrix Equations. (25th March 2014) - Yu, Juan; Wang, Qing-Wen; Dong, Chang-Zhou
Abstract : 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 A X = B, X C = D are derived, respectively. Secondly, the optimal approximation solution min ⁡ X ∈ K ⁡ ∥ X ^ - X ∥ is obtained, where K is the (anti-)Hermitian generalized (anti-)Hamiltonian solution set of the above system and X ^ 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.