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非线性特征值问题平移对称幂法的收敛率估计
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.
作者姓名:唐耀宗  杨庆之
作者单位: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
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.
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-?ojasiewicz(K-?)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.

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
Tang Yaozong,Yang Qingzhi.CONVERGENCE RATE ESTIMATION ON SS-HOPM FOR NONLINEAR EIGENVALUE PROBLEMS[J].Mathematica Numerica Sinica,2021,43(4):529-538.
Authors:Tang Yaozong  Yang Qingzhi
Institution:1. School of Mathematics and Statistics, Kashi University, Kashi 844000, China;2. School of Mathematical Sciences, Nankai University, Tianjin 300071, China
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.
Keywords:nonlinear eigenvalues  Bose-Einstein Condensation  SS-HOPM  convergence rate estimation  
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