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.
KeywordsNonlinear eigenvalue problem Successive mth approximation method Partially orthogonal projection method
Mathematics Subject Classification15A18 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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