Academic Journal
Fixed-time TGNN model with the nonlinear activation function for online solution of Sylvester tensor equation.
| Τίτλος: | Fixed-time TGNN model with the nonlinear activation function for online solution of Sylvester tensor equation. |
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| Συγγραφείς: | Xie, Mengyan, Wang, Qing-Wen, Chen, Jie |
| Πηγή: | Numerical Algorithms; Feb2026, Vol. 101 Issue 2, p1023-1047, 25p |
| Θεματικοί όροι: | Sylvester matrix equations, Artificial neural networks, Online algorithms, Numerical analysis, Mathematical proofs |
| Περίληψη: | In this work, we develop the fixed-time TGNN (tensor gradient-based neural network) model for tackling the Sylvester tensor problem ∑ n = 1 N X (t) × n A n = B online by generalizing the gradient-based design approach. We introduce a novel activation function for the TGNN model and theoretically prove its convergence. To demonstrate the superiority of our activation function, we compare it with four existing nonlinear activation functions within the TGNN model framework and provide convergence time upper bounds for each. Additionally, we validate our findings with three numerical examples. [ABSTRACT FROM AUTHOR] |
| Copyright of Numerical Algorithms is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Complementary Index |
| FullText | Links: – Type: other Text: Availability: 0 CustomLinks: – Url: https://dx.doi.org/doi:10.1007/s11075-025-02031-x Name: EDS - Springer Nature Journals (s7799221) Category: fullText Text: View record at Springer |
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| Header | DbId: edb DbLabel: Complementary Index An: 191499944 RelevancyScore: 1041 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1041.06896972656 |
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| Items | – Name: Title Label: Title Group: Ti Data: Fixed-time TGNN model with the nonlinear activation function for online solution of Sylvester tensor equation. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Xie%2C+Mengyan%22">Xie, Mengyan</searchLink><br /><searchLink fieldCode="AR" term="%22Wang%2C+Qing-Wen%22">Wang, Qing-Wen</searchLink><br /><searchLink fieldCode="AR" term="%22Chen%2C+Jie%22">Chen, Jie</searchLink> – Name: TitleSource Label: Source Group: Src Data: Numerical Algorithms; Feb2026, Vol. 101 Issue 2, p1023-1047, 25p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Sylvester+matrix+equations%22">Sylvester matrix equations</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+neural+networks%22">Artificial neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Online+algorithms%22">Online algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+proofs%22">Mathematical proofs</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this work, we develop the fixed-time TGNN (tensor gradient-based neural network) model for tackling the Sylvester tensor problem ∑ n = 1 N X (t) × n A n = B online by generalizing the gradient-based design approach. We introduce a novel activation function for the TGNN model and theoretically prove its convergence. To demonstrate the superiority of our activation function, we compare it with four existing nonlinear activation functions within the TGNN model framework and provide convergence time upper bounds for each. Additionally, we validate our findings with three numerical examples. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Numerical Algorithms is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s11075-025-02031-x Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 25 StartPage: 1023 Subjects: – SubjectFull: Sylvester matrix equations Type: general – SubjectFull: Artificial neural networks Type: general – SubjectFull: Online algorithms Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Mathematical proofs Type: general Titles: – TitleFull: Fixed-time TGNN model with the nonlinear activation function for online solution of Sylvester tensor equation. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Xie, Mengyan – PersonEntity: Name: NameFull: Wang, Qing-Wen – PersonEntity: Name: NameFull: Chen, Jie IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 10171398 Numbering: – Type: volume Value: 101 – Type: issue Value: 2 Titles: – TitleFull: Numerical Algorithms Type: main |
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