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

Xiao-Ping Chen, Wei Wei, Xi Yang, Hao Liu and Xiao-Ming Pan

Applied Mathematics and Computation, 2020, vol. 387, issue C

Abstract: 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.

Keywords: Successive linear Newton interpolation; Inexact method; Nonlinear eigenvalue problem; Locally linear convergence; Convergence factor (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:387:y:2020:i:c:s0096300319306551

DOI: 10.1016/j.amc.2019.124663

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