New perturbation bounds for the spectrum of a normal matrix

doi:10.1016/j.jmaa.2017.06.051

	New perturbation bounds for the spectrum of a normal matrix
	Xu, Xuefeng 1,2; Zhang, Chen-Song1,2
	2017-11-15
发表期刊	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN	0022-247X
卷号	455 期号:1-2 页码:1937-1955
摘要	Let A is an element of C-nxn and (A) over tilde is an element of C-nxn be two normal matrices with spectra {lambda(i)}(i=1)(n) and {(lambda) over tilde (i)}(i=1)(n) respectively. The celebrated Hoffman-Wielandt theorem states that there exists a permutation pi of {1, ... , n} such that (Sigma(n)(i=1) vertical bar(lambda) over tilde (pi(i)) - lambda(i)vertical bar(2))(1/2) is no larger than the Frobenius norm of (A) over tilde - A. However, if either A or (A) over tilde is non-normal, this result does not hold in general. In this paper, we present several novel upper bounds for (Sigma(n)(i=1) vertical bar(lambda) over tilde (pi(i)) - lambda(i)vertical bar(2))(1/2), provided that A is normal and (A) over tilde is arbitrary. Some of these estimates involving the "departure from normality" of (A) over tilde have generalized the Hoffman-Wielandt theorem. Furthermore, we give new perturbation bounds for the spectrum of a Hermitian matrix. (c) 2017 Elsevier Inc. All rights reserved.
关键词	Spectrum Perturbation Hermitian matrix Normal matrix Departure from normality
DOI	10.1016/j.jmaa.2017.06.051
语种	英语
资助项目	National Key Research and Development Program of China[2016YFB0201304] ; Major Research Plan of National Natural Science Foundation of China[91430215] ; Major Research Plan of National Natural Science Foundation of China[91530323]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000406568800060
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26304
专题	计算数学与科学工程计算研究所
通讯作者	Xu, Xuefeng
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Xu, Xuefeng,Zhang, Chen-Song. New perturbation bounds for the spectrum of a normal matrix[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2017,455(1-2):1937-1955.
APA	Xu, Xuefeng,&Zhang, Chen-Song.(2017).New perturbation bounds for the spectrum of a normal matrix.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,455(1-2),1937-1955.
MLA	Xu, Xuefeng,et al."New perturbation bounds for the spectrum of a normal matrix".JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 455.1-2(2017):1937-1955.