奇异值与特征值扰动界估计  

The Perturbation Bounds for Singular Values and Eigenvalues

作　　者：燕岩军[1] 宋儒瑛[2] 杨帆[3] YAN Yanjun;SONG Ruying;YANG Fan(Department of Public Course Teaching,Shanxi Institute of Mechanical&Electrical Engineering,Changzhi 046011,China;Department of Mathematics,Taiyuan Normal University,Taiyuan 030619,China;School of Science,Jiamusi University,Jiamusi 154002,China)

机构地区：[1]山西机电职业技术学院基础部,山西长治046011 [2]太原师范学院数学系,太原030619 [3]佳木斯大学理学院,黑龙江佳木斯154002

出　　处：《湖北民族大学学报（自然科学版）》2020年第3期309-312,共4页Journal of Hubei Minzu University:Natural Science Edition

摘　　要：基于非奇异矩阵与可对角化矩阵,主要依据矩阵奇异值分解理论及可对角化矩阵的特点,给出矩阵加法扰动下奇异值相对扰动结果和乘法扰动下特征值扰动上界.最后通过比较,说明本文得出特征值扰动结果更优,并推广了已有结果.Based on the theory of singular value decomposition of matrix and the characteristics of diagonalizable matrix.We give the perturbation bound for singular values of matrices under additive perturbations and the perturbation bound of eigenvalues under multiplicative perturbations.Finally,the comparison shows that the perturbation bound of eigenvalue in this paper is better,which generalizes the existing conclusion.

关 键 词：非奇异 可对角化 奇异值 特征值 扰动界 

分 类 号：O241.6[理学—计算数学]