An iterative method for obtaining the Least squares solutions of quadratic inverse eigenvalue problems over generalized Hamiltonian matrix with submatrix constraints

Abstract In this paper, we consider a class of constrained matrix quadratic inverse eigenvalue problem and its optimal approximation problem. It is proved that the proposed algorithm always converge to the generalized Hamiltonian solutions with a submatrix constraint of Problem 1.1 within finite iterative steps in the absence of roundoff error. In addition, by choosing a special kind of initial matrices, it is shown that the minimum norm solution of Problem 1.1 can be obtained consequently. At last, for a given matrix group in the solution set of Problem 1.1 , it is proved that the unique optimal approximation solution of Problem 1.2 can be also obtained. Some numerical results are reported to demonstrate the efficiency of our algorithm.

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