| 非线性特征值问题平移对称幂法的收敛率估计 |
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| 引用本文： | 唐耀宗,杨庆之.非线性特征值问题平移对称幂法的收敛率估计[J].计算数学,2021,43(4):529-538. |
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| 作者姓名： | 唐耀宗 杨庆之 |
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| 作者单位： | 喀什大学数学与统计学院,喀什844000;南开大学数学科学学院,天津300071 |
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| 基金项目： | 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. |
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| 摘 要： | 平移对称幂法（SS-HOPM）在求解源自玻色-爱因斯坦凝聚态的非线性特征值问题时，不仅具有较高的计算效率，而且具有点列收敛性，但其收敛率尚未得到有效估计.本文通过将多项式Kurdyka-Łojasiewicz（K-Ł）指数界的相关结果应用到所涉及优化问题的Lagrange函数上，得到了平移对称幂法的次线性收敛率估计，从理论上解释了平移对称幂法的计算效率.
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| 关 键 词： | 非线性特征值问题 玻色-爱因斯坦凝聚态 平移对称幂法 收敛率估计 |
| 收稿时间： | 2020-07-24 |
CONVERGENCE RATE ESTIMATION ON SS-HOPM FOR NONLINEAR EIGENVALUE PROBLEMS |
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| Tang Yaozong,Yang Qingzhi.CONVERGENCE RATE ESTIMATION ON SS-HOPM FOR NONLINEAR EIGENVALUE PROBLEMS[J].Mathematica Numerica Sinica,2021,43(4):529-538. |
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| Authors: | Tang Yaozong Yang Qingzhi |
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| Institution: | 1. School of Mathematics and Statistics, Kashi University, Kashi 844000, China;2. School of Mathematical Sciences, Nankai University, Tianjin 300071, China |
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| Abstract: | 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. |
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| Keywords: | nonlinear eigenvalues Bose-Einstein Condensation SS-HOPM convergence rate estimation |
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