An Extended Two-Step Method for Inverse Eigenvalue Problems with Multiple Eigenvalues

Abstract

In recent years, numerical solutions of the inverse eigenvalue problems with multiple eigenvalues have attracted the attention of some researchers, and there have been a few algorithms with quadratic convergence. We propose here an extended two-step method for solving the inverse eigenvalue problems with multiple eigenvalues. Under appropriate assumptions, the convergence analysis of the extended method is presented and the cubic root-convergence rate is proved. Numerical experiments are provided to confirm the theoretical results and comparisons with the inexact Cayley transform method are made. Our extended method and convergence result in the present paper may enrich the results of numerical solutions of the inverse eigenvalue problems with multiple eigenvalues.