AN ITERATIVE METHOD FOR THE HERMITIAN-GENERALIZED HAMILTONIAN SOLUTIONS TO THE INVERSE PROBLEM AX = B WITH A SUBMATRIX CONSTRAINT

Abstract. In this paper, an iterative method is proposed for solv- ing the matrix inverse problem AX = B for Hermitian-generalized Hamiltonian matrices with a submatrix constraint. By this iterative method, for any initial matrix A0, a solution A can be obtained in nite iteration steps in the absence of roundo errors, and the solu- tion with least norm can be obtained by choosing a special kind of initial matrix. Furthermore, in the solution set of the above prob- lem, the unique optimal approximation solution to a given matrix can also be obtained. A numerical example is presented to show the eciency of the proposed algorithm.