• 论文 •

### 非线性特征值问题平移对称幂法的收敛率估计

1. 1. 喀什大学数学与统计学院, 喀什 844000;
2. 南开大学数学科学学院, 天津 300071
• 收稿日期:2020-07-24 出版日期:2021-11-14 发布日期:2021-11-12
• 基金资助:
国家自然科学基金项目（12071234，11671217）；新疆维吾尔自治区自然科学基金面上项目（2018D01A01）资助.

Tang Yaozong, Yang Qingzhi. CONVERGENCE RATE ESTIMATION ON SS-HOPM FOR NONLINEAR EIGENVALUE PROBLEMS[J]. Mathematica Numerica Sinica, 2021, 43(4): 529-538.

### CONVERGENCE RATE ESTIMATION ON SS-HOPM FOR NONLINEAR EIGENVALUE PROBLEMS

Tang Yaozong1,2, Yang Qingzhi1,2

1. 1. School of Mathematics and Statistics, Kashi University, Kashi 844000, China;
2. School of Mathematical Sciences, Nankai University, Tianjin 300071, China
• Received:2020-07-24 Online:2021-11-14 Published:2021-11-12

In solving the nonlinear eigenvalue problems originated from Bose-Einstein Condensation, the shifted symmetric higher-order power method (SS-HOPM for short) not only has high computational efficiency, but also has point-wise convergence. However, the convergence rate of SS-HOPM has not been given. We apply the bound of the Kurdyka-Lojasiewicz (K-L) exponent of polynomial to the Lagrange function of the optimization problem involved in this paper, then we obtain sublinear convergence rate of the SS-HOPM, which can explain the calculation efficiency of the algorithm theoretically.

MR(2010)主题分类:

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