Factorizations for a class of multivariate polynomial matrices

doi:10.1007/s11045-019-00694-z

CSpace

	Factorizations for a class of multivariate polynomial matrices
	Lu, Dong 1,2; Wang, Dingkang 3,4; Xiao, Fanghui 3,4
	2020-07-01
发表期刊	MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING
ISSN	0923-6082
卷号	31 期号:3 页码:989-1004
摘要	This paper investigates how to factorize a class of multivariate polynomial matrices. We prove that an lxmmultivariate polynomial matrix admits a matrix factorization with respect to a given polynomial if the polynomial and all the (l-1)x(l-1) reduced minors of the matrix generate a unit ideal. This result is a generalization of a theorem in Liu et al. (Circuits Syst Signal Process 30(3):553-566, 2011). Based on three main theorems presented in the paper and a constructive algorithm proposed by Lin et al. (Circuits Syst Signal Process 20(6):601-618, 2001), we give an algorithm which can be used to factorize more multivariate polynomial matrices. In addition, an illustrative example is given to show the effectiveness of the proposed algorithm.
关键词	Multivariate polynomial matrices Matrix factorization Reduced minors Reduced Grobner basis
DOI	10.1007/s11045-019-00694-z
收录类别	SCI
语种	英语
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Theory & Methods ; Engineering, Electrical & Electronic
WOS记录号	WOS:000536473300010
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51514
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Dingkang
作者单位	1.Beihang Univ, Beijing Adv Innovat Ctr Big Data & Brain Comp, Beijing 100191, Peoples R China 2.Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Lu, Dong,Wang, Dingkang,Xiao, Fanghui. Factorizations for a class of multivariate polynomial matrices[J]. MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING,2020,31(3):989-1004.
APA	Lu, Dong,Wang, Dingkang,&Xiao, Fanghui.(2020).Factorizations for a class of multivariate polynomial matrices.MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING,31(3),989-1004.
MLA	Lu, Dong,et al."Factorizations for a class of multivariate polynomial matrices".MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING 31.3(2020):989-1004.