UNIT TRIANGULAR FACTORIZATION OF THE MATRIX SYMPLECTIC GROUP

doi:10.1137/19M1308839

	UNIT TRIANGULAR FACTORIZATION OF THE MATRIX SYMPLECTIC GROUP
	Jin, Pengzhan 1,2; Tang, Yifa 1,2; Zhu, Aiqing 1,2
刊名	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
	2020
卷号	41 期号:4 页码:1630-1650
关键词	symplectic symplectic matrix triangular factorization positive definite singular symplectic matrix generators parameterization unconstrained parametrization
ISSN号	0895-4798
DOI	10.1137/19M1308839
英文摘要	In this work, we prove that any symplectic matrix can be factored into no more than 9 unit triangular symplectic matrices. This structure-preserving factorization of the symplectic matrices immediately reveals two well-known features that (i) the determinant of any symplectic matrix is one and (ii) the matrix symplectic group is path connected, as well as a new feature that (iii) all the unit triangular symplectic matrices form a set of generators of the matrix symplectic group. Furthermore, this factorization yields effective methods for the unconstrained parametrization of the matrix symplectic group as well as its structured subsets. The unconstrained parametrization enables us to apply faster and more efficient unconstrained optimization algorithms to the problems with symplectic constraints under certain circumstances.
资助项目	Major Project on New Generation of Artificial Intelligence from MOST of China[2018AAA0101002] ; National Natural Science Foundation of China[11771438]
WOS研究方向	Mathematics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000600630900008
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/57913]
专题	中国科学院数学与系统科学研究院
通讯作者	Jin, Pengzhan
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, 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	Jin, Pengzhan,Tang, Yifa,Zhu, Aiqing. UNIT TRIANGULAR FACTORIZATION OF THE MATRIX SYMPLECTIC GROUP[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2020,41(4):1630-1650.
APA	Jin, Pengzhan,Tang, Yifa,&Zhu, Aiqing.(2020).UNIT TRIANGULAR FACTORIZATION OF THE MATRIX SYMPLECTIC GROUP.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,41(4),1630-1650.
MLA	Jin, Pengzhan,et al."UNIT TRIANGULAR FACTORIZATION OF THE MATRIX SYMPLECTIC GROUP".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 41.4(2020):1630-1650.