an iterative method for the hermitian-generalized hamiltonian solutions to the inverse problem ax=b with a submatrix constraint

in this paper, an iterative method is proposed for solving the matrix inverse problem $ax=b$ for hermitian-generalized hamiltonian matrices with a submatrix constraint. by this iterative method, for any initial matrix $a_0$, a solution $a^*$ can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of initial matrix. furthermore, in the solution set of the above problem, the unique optimal approximation solution to a given matrix can also be obtained. a numerical example is presented to show the efficiency of the proposed algorithm.