Complex, Temporally Variant SVD via Real ZN Method and 11-Point ZeaD Formula from Theoretics to Experiments
The complex, temporally variant singular value decomposition (SVD) problem is proposed and investigated in this paper. Firstly, the original problem is transformed into an equation system. Then, by using the real zeroing neurodynamics (ZN) method, matrix vectorization, Kronecker product, vectorized...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/11/1841 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850161083682127872 |
|---|---|
| author | Jianrong Chen Xiangui Kang Yunong Zhang |
| author_facet | Jianrong Chen Xiangui Kang Yunong Zhang |
| author_sort | Jianrong Chen |
| collection | DOAJ |
| description | The complex, temporally variant singular value decomposition (SVD) problem is proposed and investigated in this paper. Firstly, the original problem is transformed into an equation system. Then, by using the real zeroing neurodynamics (ZN) method, matrix vectorization, Kronecker product, vectorized transpose matrix, and dimensionality reduction technique, a dynamical model, termed the continuous-time SVD (CTSVD) model, is derived and investigated. Furthermore, a new 11-point Zhang et al. discretization (ZeaD) formula with fifth-order precision is proposed and studied. In addition, with the use of the 11-point and other ZeaD formulas, five discrete-time SVD (DTSVD) algorithms are further acquired. Meanwhile, theoretical analyses and numerical experimental results substantiate the correctness and convergence of the proposed CTSVD model and DTSVD algorithms. |
| format | Article |
| id | doaj-art-e8a0192f19b74c61935d00fc909f9fb8 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-e8a0192f19b74c61935d00fc909f9fb82025-08-20T02:22:58ZengMDPI AGMathematics2227-73902025-05-011311184110.3390/math13111841Complex, Temporally Variant SVD via Real ZN Method and 11-Point ZeaD Formula from Theoretics to ExperimentsJianrong Chen0Xiangui Kang1Yunong Zhang2School of Humanities and Management, Youjiang Medical University for Nationalities, Baise 533000, ChinaSchool of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, ChinaSchool of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 518107, ChinaThe complex, temporally variant singular value decomposition (SVD) problem is proposed and investigated in this paper. Firstly, the original problem is transformed into an equation system. Then, by using the real zeroing neurodynamics (ZN) method, matrix vectorization, Kronecker product, vectorized transpose matrix, and dimensionality reduction technique, a dynamical model, termed the continuous-time SVD (CTSVD) model, is derived and investigated. Furthermore, a new 11-point Zhang et al. discretization (ZeaD) formula with fifth-order precision is proposed and studied. In addition, with the use of the 11-point and other ZeaD formulas, five discrete-time SVD (DTSVD) algorithms are further acquired. Meanwhile, theoretical analyses and numerical experimental results substantiate the correctness and convergence of the proposed CTSVD model and DTSVD algorithms.https://www.mdpi.com/2227-7390/13/11/1841singular value decomposition (SVD)temporally variant matrixzeroing neurodynamics (ZN)Zhang et al. discretization (ZeaD) formula |
| spellingShingle | Jianrong Chen Xiangui Kang Yunong Zhang Complex, Temporally Variant SVD via Real ZN Method and 11-Point ZeaD Formula from Theoretics to Experiments Mathematics singular value decomposition (SVD) temporally variant matrix zeroing neurodynamics (ZN) Zhang et al. discretization (ZeaD) formula |
| title | Complex, Temporally Variant SVD via Real ZN Method and 11-Point ZeaD Formula from Theoretics to Experiments |
| title_full | Complex, Temporally Variant SVD via Real ZN Method and 11-Point ZeaD Formula from Theoretics to Experiments |
| title_fullStr | Complex, Temporally Variant SVD via Real ZN Method and 11-Point ZeaD Formula from Theoretics to Experiments |
| title_full_unstemmed | Complex, Temporally Variant SVD via Real ZN Method and 11-Point ZeaD Formula from Theoretics to Experiments |
| title_short | Complex, Temporally Variant SVD via Real ZN Method and 11-Point ZeaD Formula from Theoretics to Experiments |
| title_sort | complex temporally variant svd via real zn method and 11 point zead formula from theoretics to experiments |
| topic | singular value decomposition (SVD) temporally variant matrix zeroing neurodynamics (ZN) Zhang et al. discretization (ZeaD) formula |
| url | https://www.mdpi.com/2227-7390/13/11/1841 |
| work_keys_str_mv | AT jianrongchen complextemporallyvariantsvdviarealznmethodand11pointzeadformulafromtheoreticstoexperiments AT xianguikang complextemporallyvariantsvdviarealznmethodand11pointzeadformulafromtheoreticstoexperiments AT yunongzhang complextemporallyvariantsvdviarealznmethodand11pointzeadformulafromtheoreticstoexperiments |