Newton-like and inexact Newton-like methods for a parameterized generalized inverse eigenvalue problem

In this paper, we establish the Newton-like and inexact Newton-like based methods for solving a type of parameterized generalized inverse eigenvalue problem. This type of parameterized generalized inverse eigenvalue problem, including multiplicative and additive inverse eigenvalue problems, appears in many applications. We show that the direction produced by the Newton-like method does not depend explicitly on the eigenvalues. Also, the inexact version can minimize the oversolving problem of Newton-like methods and hence improve efficiency. We discuss the convergence properties of the presented methods. Finally, the performance and effectiveness of the algorithms are tested on three numerical examples and compared to the Newton algorithm.