Successive linear Newton interpolation methods for solving the large-scale nonlinear eigenvalue problems

摘要

We present the successive linear Newton interpolation method for solving the large-scale nonlinear eigenvalue problems, establish locally linear convergence, and give the corresponding convergence factor of the method in terms of the left and right eigenvectors in this paper. To speed up the convergence rate, we develop the modified successive linear Newton interpolation method which updates the pole simultaneously. In addition, we propose the inexact versions of the (modified) successive linear Newton interpolation method to reduce the computational cost and analyze the convergence properties. Numerical results demonstrate the effectiveness of our proposed methods.