The generalized conjugate direction method for solving quadratic inverse eigenvalue problems over generalized skew Hamiltonian matrices with a submatrix constraint

Abstract

In this paper, we consider a class of constrained quadratic inverse eigenvalue Problem 1.1. Then, a generalized conjugate direction method is proposed to obtain the generalized skew Hamiltonian matrix solutions with a submatrix constraint. In addition, by choosing a special kind of initial matrices, it is shown that the unique least Frobenius norm solutions can be obtained consequently. Some numerical results are reported to demonstrate the efficiency of our algorithm.

Keywords

• generalized conjugate direction method
• constrained matrix
• quadratic inverse eigenvalue problem
• generalized skew hamiltonian matrix
• least frobenius norm solution group