Low rank approximation of the symmetric positive semidefinite matrix

被引：6

作者：

Duan, Xuefeng ^{[1
]}

Li, Jiaofen ^{[1
]}

Wang, Qingwen ^{[2
]}

Zhang, Xinjun ^{[1
]}

机构：

[1] Guilin Univ Elect Technol, Coll Math & Computat Sci, Guilin 541004, Peoples R China

[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2014年 / 260卷

基金：

中国国家自然科学基金;

关键词：

Low rank approximation; Symmetric positive semidefinite matrix; Unconstrained optimization; Feasible set; Nonlinear conjugate gradient method; GCDS;

D O I：

10.1016/j.cam.2013.09.080

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the low rank approximation of the symmetric positive semidefinite matrix, which arises in machine learning, quantum chemistry and inverse problem. We first characterize the feasible set by X = YYT,Y is an element of R-nxk, and then transform low rank approximation into an unconstrained optimization problem. Finally, we use the nonlinear conjugate gradient method with exact line search to compute the optimal low rank symmetric positive semidefinite approximation of the given matrix. Numerical examples show that the new method is feasible and effective. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：236 / 243

页数：8

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