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非线性特征值问题平移对称幂法的收敛率估计

本站小编 Free考研考试/2021-12-27

唐耀宗1,2, 杨庆之1,2
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.

CONVERGENCE RATE ESTIMATION ON SS-HOPM FOR NONLINEAR EIGENVALUE PROBLEMS

Tang Yaozong1,2, Yang Qingzhi1,2
1. School of Mathematics and Statistics, Kashi University, Kashi 844000, China;
2. School of Mathematical Sciences, Nankai University, Tianjin 300071, China
Received:2020-07-24Online:2021-11-14Published:2021-11-12







摘要



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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.
MR(2010)主题分类:
15A18
15A69
49D37
49M99
65K05
90C26
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