Directional Secant-Type Methods for Solving Equations.
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| Title: | Directional Secant-Type Methods for Solving Equations. |
|---|---|
| Authors: | Argyros, Ioannis1 ioannisa@cameron.edu, Hilout, Saïd2 said.hilout@math.univ-poitiers.fr |
| Source: | Journal of Optimization Theory & Applications. May2013, Vol. 157 Issue 2, p462-485. 24p. |
| Subjects: | Secant function, Nonlinear equations, Lipschitz spaces, Hypothesis, Hilbert space, Stochastic partial differential equations |
| Abstract: | A semilocal convergence analysis for directional Secant-type methods in multidimensional space is provided. Using weaker hypotheses than the ones exploited by An and Bai, we provide a semilocal convergence analysis with the following advantages: weaker convergence conditions, larger convergence domain, finer error estimates on the distances involved, and more precise information on the location of the solution. A numerical example, where our results apply to solve an equation but not the ones of An and Bai, is also provided. In a second example, we show how to implement the method. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Optimization Theory & Applications 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.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 87086629 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Directional Secant-Type Methods for Solving Equations. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Argyros%2C+Ioannis%22">Argyros, Ioannis</searchLink><relatesTo>1</relatesTo><i> ioannisa@cameron.edu</i><br /><searchLink fieldCode="AR" term="%22Hilout%2C+Saïd%22">Hilout, Saïd</searchLink><relatesTo>2</relatesTo><i> said.hilout@math.univ-poitiers.fr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Optimization+Theory+%26+Applications%22">Journal of Optimization Theory & Applications</searchLink>. May2013, Vol. 157 Issue 2, p462-485. 24p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Secant+function%22">Secant function</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+equations%22">Nonlinear equations</searchLink><br /><searchLink fieldCode="DE" term="%22Lipschitz+spaces%22">Lipschitz spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Hypothesis%22">Hypothesis</searchLink><br /><searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+partial+differential+equations%22">Stochastic partial differential equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A semilocal convergence analysis for directional Secant-type methods in multidimensional space is provided. Using weaker hypotheses than the ones exploited by An and Bai, we provide a semilocal convergence analysis with the following advantages: weaker convergence conditions, larger convergence domain, finer error estimates on the distances involved, and more precise information on the location of the solution. A numerical example, where our results apply to solve an equation but not the ones of An and Bai, is also provided. In a second example, we show how to implement the method. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Optimization Theory & Applications 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/s10957-012-0104-8 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 24 StartPage: 462 Subjects: – SubjectFull: Secant function Type: general – SubjectFull: Nonlinear equations Type: general – SubjectFull: Lipschitz spaces Type: general – SubjectFull: Hypothesis Type: general – SubjectFull: Hilbert space Type: general – SubjectFull: Stochastic partial differential equations Type: general Titles: – TitleFull: Directional Secant-Type Methods for Solving Equations. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Argyros, Ioannis – PersonEntity: Name: NameFull: Hilout, Saïd IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2013 Type: published Y: 2013 Identifiers: – Type: issn-print Value: 00223239 Numbering: – Type: volume Value: 157 – Type: issue Value: 2 Titles: – TitleFull: Journal of Optimization Theory & Applications Type: main |
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