### CONVERGENCE ANALYSIS ON SS-HOPM FOR BEC-LIKE NONLINEAR EIGENVALUE PROBLEMS

Yaozong Tang1,2, Qingzhi Yang1,2, Gang Luo1

1. 1 School of Mathematical Sciences, LPMC, Nankai University, Tianjin 300071, China;
2 School of Mathematics and Statistics, Kashi University, Kashi 844006, China
• Received:2019-12-18 Revised:2020-03-16 Online:2021-07-15 Published:2021-08-06
• Contact: Qingzhi Yang,Email:qz-yang@nankai.edu.cn
• Supported by:
We are grateful to the referees for their insightful comments and suggestions. This work is supported by Natural Science Foundation of XinJiang (Grant No. 2018D01A01).

Yaozong Tang, Qingzhi Yang, Gang Luo. CONVERGENCE ANALYSIS ON SS-HOPM FOR BEC-LIKE NONLINEAR EIGENVALUE PROBLEMS[J]. Journal of Computational Mathematics, 2021, 39(4): 621-632.

Shifted symmetric higher-order power method (SS-HOPM) has been proved effective in solving the nonlinear eigenvalue problem oriented from the Bose-Einstein Condensation (BEC-like NEP for short) both theoretically and numerically. However, the convergence of the sequence generated by SS-HOPM is based on the assumption that the real eigenpairs of BEC-like NEP are finite. In this paper, we will establish the point-wise convergence via Lojasiewicz inequality by introducing a new related sequence.

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