非线性特征值问题平移对称幂法的收敛率估计  

CONVERGENCE RATE ESTIMATION ON SS-HOPM FOR NONLINEAR EIGENVALUE PROBLEMS

作　　者：唐耀宗 杨庆之 Tang Yaozong;Yang Qingzhi(School of Mathematics and Statistics,Kashi University,Kashi 844000,China;School of Mathematical Sciences,Nankai University,Tianjin 300071,China)

机构地区：[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

出　　处：《计算数学》2021年第4期529-538,共10页Mathematica Numerica Sinica

基　　金：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-Lojasiewicz(K-L)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.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.

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 

分 类 号：O224[理学—运筹学与控制论] O469[理学—数学]