Smallest Singular Value Based Newton-Like Methods for Solving Quadratic Inverse Eigenvalue Problem

Abstract

A Newton method for solving quadratic inverse eigenvalue problems is proposed. The method is based on the properties of the smallest singular value of a matrix. In order to reduce computational cost, we use approximations of the smallest singular value and the corresponding unit left and right singular vectors obtained by the one-step inverse iteration. It is shown that both the proposed method and its modification have locally quadratic convergence. Numerical results confirm theoretical findings and demonstrate the effectiveness of the methods proposed.