A Globally Convergent Inexact Newton-Like Cayley Transform Method for Inverse Eigenvalue Problems

TL;DR

This paper introduces a globally convergent inexact Newton-like method utilizing Cayley transforms for solving inverse eigenvalue problems, with proven convergence properties and demonstrated effectiveness through numerical examples.

Contribution

The paper develops a new inexact Newton-like method with global convergence analysis specifically for inverse eigenvalue problems, enhancing solution reliability.

Findings

Effective in solving IEP with distinct eigenvalues

Global convergence of the proposed method is established

Numerical results confirm high efficiency

Abstract

We propose a inexact Newton method for solving inverse eigenvalue problems (IEP). This method is globalized by employing the classical backtracking techniques. A global convergence analysis of this method is provided and the R-order convergence property is proved under some mild assumptions. Numerical examples demonstrate that the proposed method is very effective for solving the IEP with distinct eigenvalues.