UNIT TRIANGULAR FACTORIZATION OF THE MATRIX SYMPLECTIC GROUP

doi:10.1137/19M1308839

CSpace

	UNIT TRIANGULAR FACTORIZATION OF THE MATRIX SYMPLECTIC GROUP
	Jin, Pengzhan 1,2; Tang, Yifa 1,2; Zhu, Aiqing 1,2
	2020
发表期刊	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN	0895-4798
卷号	41 期号:4 页码:1630-1650
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.
关键词	symplectic symplectic matrix triangular factorization positive definite singular symplectic matrix generators parameterization unconstrained parametrization
DOI	10.1137/19M1308839
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000600630900008
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/57914
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.