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.
Cai, J. (2013). An iterative method for the Hermitian-generalized Hamiltonian solutions to the inverse problem AX=B with a submatrix constraint. Bulletin of the Iranian Mathematical Society, 39(6), 1249-1260.
MLA
J. Cai. "An iterative method for the Hermitian-generalized Hamiltonian solutions to the inverse problem AX=B with a submatrix constraint". Bulletin of the Iranian Mathematical Society, 39, 6, 2013, 1249-1260.
HARVARD
Cai, J. (2013). 'An iterative method for the Hermitian-generalized Hamiltonian solutions to the inverse problem AX=B with a submatrix constraint', Bulletin of the Iranian Mathematical Society, 39(6), pp. 1249-1260.
VANCOUVER
Cai, J. An iterative method for the Hermitian-generalized Hamiltonian solutions to the inverse problem AX=B with a submatrix constraint. Bulletin of the Iranian Mathematical Society, 2013; 39(6): 1249-1260.