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UNIT TRIANGULAR FACTORIZATION OF THE MATRIX SYMPLECTIC GROUP

文献类型：期刊论文

作者Jin, Pengzhan1,2; Tang, Yifa1,2; Zhu, Aiqing1,2
刊名SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
出版日期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
DOI10.1137/19M1308839
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
WOS记录号WOS:000600630900008
出版者SIAM PUBLICATIONS
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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