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	Some perturbation results for a normalized Non-Orthogonal Joint Diagonalization problem
	Shi, De-cai ; Cal, Yun-feng ; Xu, Shu-fang
	2015
关键词	Joint diagonalization Simultaneous diagonalization Perturbation analysis BLIND SOURCE SEPARATION OPTIMIZATION
英文摘要	Non-Orthogonal Joint Diagonalization (NOJD) of a given real symmetric matrix set A = {A(j)}(j=0)(p) is to find a nonsingular matrix W such that W-T A(j)W for j = 0, 1, ... ,p are all as diagonal as possible. If the columns of the solution W are all required to be unit length, we call such NOJD problem as the Normalized NOJD (NNOJD) problem. In this paper, we discuss the perturbation theory for NNOJD as an optimization problem. Based on the perturbation analysis of general constrained optimization problem given in [16], we obtain an upper bound for the distance between an approximated solution of the perturbed optimal problem and the set of exact joint diagonalizers. As corollaries, a perturbation bound and an error bound are also given. Numerical examples validate the bounds. (C) 2015 Elsevier Inc. All rights reserved.; NSFC [11301013]; SCI(E); EI; ARTICLE; decaishi@gmail.com; yfcai@math.pku.edu.cn; xsf@pku.edu.cn; 457-476; 484
语种	中文
出处	SCI ; EI
出版者	LINEAR ALGEBRA AND ITS APPLICATIONS
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/415506]
专题	数学科学学院
推荐引用方式 GB/T 7714	Shi, De-cai,Cal, Yun-feng,Xu, Shu-fang. Some perturbation results for a normalized Non-Orthogonal Joint Diagonalization problem. 2015-01-01.

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