New remarks on the factorization and equivalence problems for a class of multivariate polynomial matrices

doi:10.1016/j.jsc.2022.07.005

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	New remarks on the factorization and equivalence problems for a class of multivariate polynomial matrices
	Lu, Dong 1,2; Wang, Dingkang 3,4; Xiao, Fanghui 5
	2023-03-01
发表期刊	JOURNAL OF SYMBOLIC COMPUTATION
ISSN	0747-7171
卷号	115 页码:266-284
摘要	This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain a necessary and sufficient condition for the equivalence of a square polynomial matrix and a diagonal matrix. Based on the constructive proof of the new criteria, we give a factorization algorithm and prove the uniqueness of the factorization. We implement the algorithm on Maple, and two illustrative examples are given to show the effectiveness of the algorithm. (c) 2022 Elsevier Ltd. All rights reserved.
关键词	Multivariate polynomial matrices Matrix factorization Matrix equivalence Column reduced minors Gr?bner basis
DOI	10.1016/j.jsc.2022.07.005
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[12001030] ; National Natural Science Foundation of China[12171469] ; CAS Key Project[QYZDJ-SSW-SYS022] ; National Key Research and Development Project[2020YFA0712300]
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Theory & Methods ; Mathematics, Applied
WOS记录号	WOS:000860188200012
出版者	ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60942
专题	中国科学院数学与系统科学研究院
通讯作者	Lu, Dong
作者单位	1.Southwest Jiaotong Univ, Sch Math, Chengdu 610031, 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 5.Hunan Normal Univ, Sch Math & Stat, LCSM, MOE, Changsha 410081, Peoples R China
推荐引用方式 GB/T 7714	Lu, Dong,Wang, Dingkang,Xiao, Fanghui. New remarks on the factorization and equivalence problems for a class of multivariate polynomial matrices[J]. JOURNAL OF SYMBOLIC COMPUTATION,2023,115:266-284.
APA	Lu, Dong,Wang, Dingkang,&Xiao, Fanghui.(2023).New remarks on the factorization and equivalence problems for a class of multivariate polynomial matrices.JOURNAL OF SYMBOLIC COMPUTATION,115,266-284.
MLA	Lu, Dong,et al."New remarks on the factorization and equivalence problems for a class of multivariate polynomial matrices".JOURNAL OF SYMBOLIC COMPUTATION 115(2023):266-284.