A RIEMANNIAN NEWTON ALGORITHM FOR NONLINEAR EIGENVALUE PROBLEMS

被引：45

作者：

Zhao, Zhi ^{[1
]}

Bai, Zheng-Jian ^{[2
]}

Jin, Xiao-Qing ^{[1
]}

机构：

[1] Univ Macau, Dept Math, Macau, Peoples R China

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2015年 / 36卷 / 02期

基金：

中国国家自然科学基金;

关键词：

nonlinear eigenvalue problem; Riemannian Newton algorithm; Stiefel manifold; Grassmann manifold; TRUST-REGION METHODS; TOTAL-ENERGY CALCULATIONS; MOLECULAR-DYNAMICS; HARTREE-FOCK; OPTIMIZATION; MINIMIZATION; FUNCTIONALS; MANIFOLDS; GEOMETRY;

D O I：

10.1137/140967994

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give the formulation of a Riemannian Newton algorithm for solving a class of nonlinear eigenvalue problems by minimizing a total energy function subject to the orthogonality constraint. Under some mild assumptions, we establish the global and quadratic convergence of the proposed method. Moreover, the positive definiteness condition of the Riemannian Hessian of the total energy function at a solution is derived. Some numerical tests are reported to illustrate the efficiency of the proposed method for solving large-scale problems.

引用

页码：752 / 774

页数：23

共 46 条

[1] PROJECTION-LIKE RETRACTIONS ON MATRIX MANIFOLDS [J].