Modifications of higher-order convergence for solving nonlinear equations
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| Title: | Modifications of higher-order convergence for solving nonlinear equations |
|---|---|
| Authors: | Liu, Xi-Lan1,2 doclanliu2002@yahoo.com.cn, Wang, Xiao-Rui1 |
| Source: | Journal of Computational & Applied Mathematics. Jul2011, Vol. 235 Issue 17, p5105-5111. 7p. |
| Subjects: | Stochastic convergence, Numerical solutions to nonlinear differential equations, Newton-Raphson method, Mathematical analysis, Iterative methods (Mathematics) |
| Abstract: | Abstract: In [Liang Fang, Guoping He, Some modifications of Newton’s method with higher-order convergence for solving nonlinear equations, J. Comput. Appl. Math. 228 (2009) 296–303], the authors pointed out that the iteration constructed in [Y.M. Ham, C.B. Chun and S.G. Lee, Some higher-order modifications of Newton’s method for solving nonlinear equations, J. Comput. Appl. Math. 222 (2008) 477–486] failed when . They gave some counterexamples and obtained a modified result. However, they did not show the essential reason which leads to the incorrect result. In this paper, we shall show that reason and present more general results than the above-mentioned papers. [Copyright &y& Elsevier] |
| Copyright of Journal of Computational & Applied Mathematics is the property of Elsevier B.V. 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 | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 62271017 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Modifications of higher-order convergence for solving nonlinear equations – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Liu%2C+Xi-Lan%22">Liu, Xi-Lan</searchLink><relatesTo>1,2</relatesTo><i> doclanliu2002@yahoo.com.cn</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Xiao-Rui%22">Wang, Xiao-Rui</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+%26+Applied+Mathematics%22">Journal of Computational & Applied Mathematics</searchLink>. Jul2011, Vol. 235 Issue 17, p5105-5111. 7p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Stochastic+convergence%22">Stochastic convergence</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+nonlinear+differential+equations%22">Numerical solutions to nonlinear differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Newton-Raphson+method%22">Newton-Raphson method</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Abstract: In [Liang Fang, Guoping He, Some modifications of Newton’s method with higher-order convergence for solving nonlinear equations, J. Comput. Appl. Math. 228 (2009) 296–303], the authors pointed out that the iteration constructed in [Y.M. Ham, C.B. Chun and S.G. Lee, Some higher-order modifications of Newton’s method for solving nonlinear equations, J. Comput. Appl. Math. 222 (2008) 477–486] failed when . They gave some counterexamples and obtained a modified result. However, they did not show the essential reason which leads to the incorrect result. In this paper, we shall show that reason and present more general results than the above-mentioned papers. [Copyright &y& Elsevier] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Computational & Applied Mathematics is the property of Elsevier B.V. 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: 10.1016/j.cam.2011.04.039 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: 5105 Subjects: – SubjectFull: Stochastic convergence Type: general – SubjectFull: Numerical solutions to nonlinear differential equations Type: general – SubjectFull: Newton-Raphson method Type: general – SubjectFull: Mathematical analysis Type: general – SubjectFull: Iterative methods (Mathematics) Type: general Titles: – TitleFull: Modifications of higher-order convergence for solving nonlinear equations Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Liu, Xi-Lan – PersonEntity: Name: NameFull: Wang, Xiao-Rui IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2011 Type: published Y: 2011 Identifiers: – Type: issn-print Value: 03770427 Numbering: – Type: volume Value: 235 – Type: issue Value: 17 Titles: – TitleFull: Journal of Computational & Applied Mathematics Type: main |
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