A Two‐Step Method for Parameterized Generalized Inverse Eigenvalue Problem

ABSTRACT In this paper, we investigate the numerical solutions of the parameterized generalized inverse eigenvalue problem which is widely applicable in many fields such as structural engineering, mechanics, and physics. Motivated by the iterative procedure for solving general nonlinear equations, we propose here a two‐step method for solving the parameterized generalized inverse eigenvalue problem, which has a higher convergence rate compared with other existing methods. Under some mild conditions, we establish a local convergence result for the proposed method and prove the cubic convergence property. To demonstrate the effectiveness of the proposed method, we present some numerical examples and comparisons with other methods are also made.