Computational and Applied Mathematics

, Volume 36, Issue 2, pp 1009–1021 | Cite as

Successive mth approximation method for the nonlinear eigenvalue problem



In this paper, we propose a successive mth (\(m\ge 2\)) approximation method for the nonlinear eigenvalue problem (NEP) and analyze its local convergence. Applying the partially orthogonal projection method to the successive mth approximation problem, we present the partially orthogonal projection method with the successive mth approximation for solving the NEP. Numerical experiments are reported to illustrate the effectiveness of the proposed methods.


Nonlinear eigenvalue problem Successive mth approximation method Partially orthogonal projection method 

Mathematics Subject Classification

15A18 65F15 



The authors would like to express their heartfelt thanks to Professor Jinyun Yuan and anonymous referees for their useful comments and suggestions which helped to improve the presentation of this paper. The work is supported by the National Natural Science Foundation of China under Grant No. 11571171 and No. 11401305, the Natural Science Foundation of Jiangsu Province of China under grant BK20141408, and the Fundamental Research Funds for the Central Universities No. NZ2014101. We would like to thank Dr. Jianhua Zhang for his helpful suggestions.


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© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2015

Authors and Affiliations

  1. 1.College of ScienceNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.College of JinchengNanjing University of Aeronautics and AstronauticsNanjingChina

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