A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations.
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| Title: | A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations. |
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| Authors: | Waziri, M. Y.1,2 mywaziri@gmail.com, Leong, W. J.1, Mamat, M.3 |
| Source: | Journal of Applied Mathematics. 2012, p1-9. 9p. |
| Subjects: | Matrices (Mathematics), Secant function, Nonlinear equations, Performance evaluation, Analysis of variance, Numerical solutions to differential equations, Mathematical forms |
| Abstract: | We propose an approach to enhance the performance of a diagonal variant of secant method for solving large-scale systems of nonlinear equations. In this approach, we consider diagonal secant method using data from two preceding steps rather than a single step derived using weak secant equation to improve the updated approximate Jacobian in diagonal form. The numerical results verify that the proposed approach is a clear enhancement in numerical performance. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell 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 |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 84861671 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Waziri%2C+M%2E+Y%2E%22">Waziri, M. Y.</searchLink><relatesTo>1,2</relatesTo><i> mywaziri@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Leong%2C+W%2E+J%2E%22">Leong, W. J.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Mamat%2C+M%2E%22">Mamat, M.</searchLink><relatesTo>3</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mathematics%22">Journal of Applied Mathematics</searchLink>. 2012, p1-9. 9p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br /><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="%22Performance+evaluation%22">Performance evaluation</searchLink><br /><searchLink fieldCode="DE" term="%22Analysis+of+variance%22">Analysis of variance</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+differential+equations%22">Numerical solutions to differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+forms%22">Mathematical forms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We propose an approach to enhance the performance of a diagonal variant of secant method for solving large-scale systems of nonlinear equations. In this approach, we consider diagonal secant method using data from two preceding steps rather than a single step derived using weak secant equation to improve the updated approximate Jacobian in diagonal form. The numerical results verify that the proposed approach is a clear enhancement in numerical performance. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell 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: 10.1155/2012/348654 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 9 StartPage: 1 Subjects: – SubjectFull: Matrices (Mathematics) Type: general – SubjectFull: Secant function Type: general – SubjectFull: Nonlinear equations Type: general – SubjectFull: Performance evaluation Type: general – SubjectFull: Analysis of variance Type: general – SubjectFull: Numerical solutions to differential equations Type: general – SubjectFull: Mathematical forms Type: general Titles: – TitleFull: A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Waziri, M. Y. – PersonEntity: Name: NameFull: Leong, W. J. – PersonEntity: Name: NameFull: Mamat, M. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2012 Type: published Y: 2012 Identifiers: – Type: issn-print Value: 1110757X Titles: – TitleFull: Journal of Applied Mathematics Type: main |
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