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

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.