Premium
Two‐step Newton‐type methods for solving inverse eigenvalue problems
Author(s) -
Chen Xiao Shan,
Wen Chao Tao,
Sun Haiwei
Publication year - 2018
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2185
Subject(s) - newton's method , mathematics , newton's method in optimization , newton fractal , eigenvalues and eigenvectors , quadratic growth , inverse , steffensen's method , inverse iteration , convergence (economics) , local convergence , iterative method , mathematical optimization , algorithm , nonlinear system , geometry , physics , quantum mechanics , economics , economic growth
Summary In this paper, we apply the two‐step Newton method to solve inverse eigenvalue problems, including exact Newton, Newton‐like, and inexact Newton‐like versions. Our results show that both two‐step Newton and two‐step Newton‐like methods converge cubically, and the two‐step inexact Newton‐like method is super quadratically convergent. Numerical implementations demonstrate the effectiveness of new algorithms.