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	A MATRIX POLYNOMIAL SPECTRAL APPROACH FOR GENERAL JOINT BLOCK DIAGONALIZATION
	Cai, Yunfeng ; Shi, Decai ; Xu, Shufang
	2015
关键词	general joint block diagonalization matrix polynomial tensor decomposition BLIND SOURCE SEPARATION INDEPENDENT COMPONENT ANALYSIS CONVOLUTIVE MIXTURES SIGNAL SEPARATION FAST ALGORITHM
英文摘要	Joint block diagonalization (JBD) of a given Hermitian matrix set {A(i)}(i=0)(p) is to find a nonsingular matrix W such that W-H A(i)W for i = 0, 1, ... , p are all block diagonal matrices with the same prescribed block diagonal structure. General JBD (GJBD) attempts to solve JBD without knowing the resulting block diagonal structure in advance, which is more difficult than JBD. In this paper, we reveal that GJBD of {A(i)}(i=0)(p) is strongly connected with the spectral information of the corresponding matrix polynomial P(lambda) = Sigma(p)(i= 0) lambda(i)A(i). Under some conditions, the solutions to GJBD are characterized by the spectral information, and a necessary and sufficient condition is given for the existence of nontrivial solutions to GJBD. In addition, based on the established theory, two feasible numerical methods are proposed to solve GJBD.; NSFC [61075119, 11301013]; SCI(E); EI; ARTICLE; yfcai@math.pku.edu.cn; decaishi@gmail.com; xsf@math.pku.edu.cn; 2; 839-863; 36
语种	英语
出处	SCI ; EI
出版者	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/421165]
专题	数学科学学院
推荐引用方式 GB/T 7714	Cai, Yunfeng,Shi, Decai,Xu, Shufang. A MATRIX POLYNOMIAL SPECTRAL APPROACH FOR GENERAL JOINT BLOCK DIAGONALIZATION. 2015-01-01.

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