解大型对称矩阵特征值问题的一个子空间加速截断牛顿法

J4 ›› 2011, Vol. 46 ›› Issue (8): 8-12.

解大型对称矩阵特征值问题的一个子空间加速截断牛顿法

钱小燕

南京工业大学理学院, 江苏南京 210009

收稿日期:2010-10-20 出版日期:2011-08-20 发布日期:2011-09-08
作者简介:钱小燕(1976- ),女,硕士,讲师,研究方向为计算数学. Email:xyqian122@163.com
基金资助:
国家自然科学基金资助项目(71071075);南京工业大学青年教师学术基金资助项目(39704017)

A subspace accelerated truncated Newton algorithm for solving the extreme eigenvalue of large-scale sparse symmetric matrix

QIAN Xiao-yan

College of Science, Nanjing University of Technology, Nanjing 210009, Jiangsu, China

Received:2010-10-20 Online:2011-08-20 Published:2011-09-08

摘要/Abstract

摘要：

基于非线性优化中的截断牛顿法提出了解大型稀疏对称矩阵特征值问题的一个子空间加速的截断牛顿法,证明了算法的收敛性并进行了数值试验,数值试验结果表明数值结果与理论分析相符,表明该算法是有效的。

关键词: 对称矩阵;特征值;特征向量;截断牛顿法;子空间加速法

Abstract:

Based on the classic truncated Newton algorithm for nonlinear optimization, a new subspace accelerated truncated Newton algorithm is presented for large-scale symmetric sparse extreme eigenvalue problems. The convergence properties are proved and numerical experiments are done. The numerical results match the convergence analysis,which showing the new algorithm is effective.

Key words: symmetric matrix; eigenvalue; eigen-vector; truncated Newton method; subspace accelerated method

钱小燕. 解大型对称矩阵特征值问题的一个子空间加速截断牛顿法[J]. J4, 2011, 46(8): 8-12.

QIAN Xiao-yan. A subspace accelerated truncated Newton algorithm for solving the extreme eigenvalue of large-scale sparse symmetric matrix[J]. J4, 2011, 46(8): 8-12.

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