A New Adaptive Multi-step Levenberg-Marquardt Method and its Improved Convergence Results.
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| Title: | A New Adaptive Multi-step Levenberg-Marquardt Method and its Improved Convergence Results. |
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| Authors: | Meilan Zeng1 zml571@126.com, Junchao Zhou2 zhoujunchao@hbeu.edu.cn |
| Source: | IAENG International Journal of Computer Science. Aug2025, Vol. 52 Issue 8, p2605-2611. 7p. |
| Subjects: | Nonlinear equations, Marquardt algorithm, Iterative methods (Mathematics), Quantitative research, Asymptotic expansions, Holder spaces |
| Abstract: | In this paper, we propose an adaptive multi-step Levenberg-Marquardt (LM) method with a new parameter λk = μkkGT k Fkkδ; δ∊ 2 (0; 1] for solving nonlinear equations and improve convergence results. The global and local convergence theories are established. The local superlinear convergence is proved under the Hölderian local error bound condition, which is weaker than the local error bound. Numerical experiments verify the convergence of our algorithm for singular problems that satisfy the Hölderian local error bound condition. [ABSTRACT FROM AUTHOR] |
| Copyright of IAENG International Journal of Computer Science is the property of International Association of Engineers (IAENG) 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.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 187082372 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A New Adaptive Multi-step Levenberg-Marquardt Method and its Improved Convergence Results. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Meilan+Zeng%22">Meilan Zeng</searchLink><relatesTo>1</relatesTo><i> zml571@126.com</i><br /><searchLink fieldCode="AR" term="%22Junchao+Zhou%22">Junchao Zhou</searchLink><relatesTo>2</relatesTo><i> zhoujunchao@hbeu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Computer+Science%22">IAENG International Journal of Computer Science</searchLink>. Aug2025, Vol. 52 Issue 8, p2605-2611. 7p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Nonlinear+equations%22">Nonlinear equations</searchLink><br /><searchLink fieldCode="DE" term="%22Marquardt+algorithm%22">Marquardt algorithm</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Quantitative+research%22">Quantitative research</searchLink><br /><searchLink fieldCode="DE" term="%22Asymptotic+expansions%22">Asymptotic expansions</searchLink><br /><searchLink fieldCode="DE" term="%22Holder+spaces%22">Holder spaces</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, we propose an adaptive multi-step Levenberg-Marquardt (LM) method with a new parameter λk = μkkGT k Fkkδ; δ∊ 2 (0; 1] for solving nonlinear equations and improve convergence results. The global and local convergence theories are established. The local superlinear convergence is proved under the Hölderian local error bound condition, which is weaker than the local error bound. Numerical experiments verify the convergence of our algorithm for singular problems that satisfy the Hölderian local error bound condition. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IAENG International Journal of Computer Science is the property of International Association of Engineers (IAENG) 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: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: 2605 Subjects: – SubjectFull: Nonlinear equations Type: general – SubjectFull: Marquardt algorithm Type: general – SubjectFull: Iterative methods (Mathematics) Type: general – SubjectFull: Quantitative research Type: general – SubjectFull: Asymptotic expansions Type: general – SubjectFull: Holder spaces Type: general Titles: – TitleFull: A New Adaptive Multi-step Levenberg-Marquardt Method and its Improved Convergence Results. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Meilan Zeng – PersonEntity: Name: NameFull: Junchao Zhou IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: Aug2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 1819656X Numbering: – Type: volume Value: 52 – Type: issue Value: 8 Titles: – TitleFull: IAENG International Journal of Computer Science Type: main |
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