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| 一类Hermitian鞍点矩阵的特征值估计 | |
| 引用本文： | 黄娜,马昌凤,谢亚君.一类Hermitian鞍点矩阵的特征值估计[J].计算数学,2015,37(1):92-102. |
| 作者姓名： | 黄娜 马昌凤 谢亚君 |
| 作者单位： | 1. 福建师范大学数学与计算机科学学院, 福州 350117; 2. 福建江夏学院数理系, 福州 350108 |
| 基金项目： | 国家自然科学基金(11071041,11201074)资助项目;福建省自然科学基金(2013J01037)资助项目. |
| 摘 要： | 本文研究了一类大型稀疏Hermitian鞍点线性系统Az=(B E E* 0)(x y)=(f g)=b系数矩阵的特征值,其中B∈C~(p×p)是Hermitian正定阵矩阵,E∈C~(p×q)是列降秩.本文分别给出了该系数矩阵正特征值与负特征值界的一个估计式,同时通过数值算例验证本文所给出的特征值界的估计是合理且有效的. |
| 关 键 词： | 鞍点问题 Hermitian 矩阵 奇异 特征值估计 |
| 收稿时间： | 2014-04-13; |
ON ESTIMATION OF THE EIGENVALUES FOR A CLASS OF HERMITIAN SADDLE POINT MATRICES |
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| Huang Na,Ma Changfeng,Xie Yajun.ON ESTIMATION OF THE EIGENVALUES FOR A CLASS OF HERMITIAN SADDLE POINT MATRICES[J].Mathematica Numerica Sinica,2015,37(1):92-102. | |
| Authors: | Huang Na Ma Changfeng Xie Yajun |
| Institution: | 1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350117, China; 2. Department of Mathematics and Physics, Fujian Jiangxia University, Fuzhou 350108, China |
| Abstract: | In this paper, we consider the eigenvalues of the coefficient matrix on a class of the large, sparse and Hermitian system of linear equations Az≡(E*B 0E)(yx)=(gf)≡b, where B∈Cp×p is Hermitian positive definite and E∈Cp×p is deficient column rank. And we derive the positive eigenvalue bounds and the negative eigenvalue bounds of the coefficient matrix, respectively. Moreover, we give a numerical example to show the rationality and effectiveness of the eigenvalue bounds. |
| Keywords: | saddle point problem Hermitian matrix singular eigenvalue estimates |
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