KMS Of Academy of mathematics and systems sciences, CAS
| UNIT TRIANGULAR FACTORIZATION OF THE MATRIX SYMPLECTIC GROUP | |
| Jin, Pengzhan1,2; Tang, Yifa1,2; Zhu, Aiqing1,2 | |
| 2020 | |
| Source Publication | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
 |
| ISSN | 0895-4798 |
| Volume | 41Issue:4Pages:1630-1650 |
| Abstract | 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. |
| Keyword | symplectic symplectic matrix triangular factorization positive definite singular symplectic matrix generators parameterization unconstrained parametrization |
| DOI | 10.1137/19M1308839 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | Major Project on New Generation of Artificial Intelligence from MOST of China[2018AAA0101002] ; National Natural Science Foundation of China[11771438] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000600630900008 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/57914 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Jin, Pengzhan |
| Affiliation | 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 |
| Recommended Citation 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. |
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