Matrix LSQR algorithms for solving constrained quadratic inverse eigenvalue problem

Abstract

The inverse eigenvalue problem appears in many applications such as control design, seismic tomography, exploration and remote sensing, molecular spectroscopy, particle physics, structural analysis, and mechanical system simulation. This paper investigates the matrix form of LSQR methods for solving the quadratic inverse eigenvalue problem with partially bisymmetric matrices under a prescribed submatrix constraint. In order to illustrate the effectiveness and feasibility of our results, one numerical example is presented.