(Anti-)‎Hermitian Generalized (Anti-)‎Hamiltonian Solution to a System of Matrix Equations

Abstract EN

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 minX∈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.