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...

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Main Authors: Jianrong Chen, Xiangui Kang, Yunong Zhang
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/11/1841
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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.
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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
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AT xianguikang complextemporallyvariantsvdviarealznmethodand11pointzeadformulafromtheoreticstoexperiments
AT yunongzhang complextemporallyvariantsvdviarealznmethodand11pointzeadformulafromtheoreticstoexperiments