A LANCZOS METHOD FOR LARGE-SCALE EXTREME LORENTZ EIGENVALUE PROBLEMS

被引：8
|
作者：
Zhang, Lei-Hong [1 ,2 ]
Shen, Chungen [3 ]
Yang, Wei Hong [4 ]
Judice, Joaquim J. [5 ]
机构：
[1] Shanghai Univ Finance & Econ, Sch Math, Shanghai 200433, Peoples R China
[2] Shanghai Univ Finance & Econ, Res Sch Interdisciplinary Sci, Shanghai 200433, Peoples R China
[3] Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China
[4] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
[5] Univ Coimbra, Inst Telecomunicacoes, Polo 2, P-3030290 Coimbra, Portugal
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2018年 / 39卷 / 02期
基金：
中国国家自然科学基金;
关键词：
eigenvalue problem; eigenvalue complementarity problem; copositivity; second-order cone problem; TRUST-REGION SUBPROBLEM; COMPLEMENTARITY-PROBLEM; CONVERGENCE;
D O I：
10.1137/17M1111401
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we are concerned with an efficient algorithm for solving the extreme Lorentz eigenvalue problem (ELE). The Lorentz eigenvalue problem is an eigenvalue complementarity problem over the Lorentz cone, and solving ELE is equivalent to testing the Lorentz-copositivity for a given matrix. Treating ELE as a special eigenvalue problem, we propose a Lanczos-type method which mimics the Rayleigh-Ritz procedure and is suitable for large-scale and sparse problems. The numerical behavior and efficiency of the proposed method are supported by the theoretical convergence results and some preliminary numerical experiments.
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页码：611 / 631
页数：21
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