Some New Variants of Cauchy's Methods for Solving Nonlinear Equations
We present and analyze some variants of Cauchy's methods free from second derivative for obtaining simple roots of nonlinear equations. The convergence analysis of the methods is discussed. It is established that the methods have convergence order three. Per iteration the new methods require tw...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/927450 |
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| _version_ | 1832558227836895232 |
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| author | Tianbao Liu Hengyan Li |
| author_facet | Tianbao Liu Hengyan Li |
| author_sort | Tianbao Liu |
| collection | DOAJ |
| description | We present and analyze some variants of Cauchy's methods free from
second derivative for obtaining simple roots of nonlinear equations. The convergence
analysis of the methods is discussed. It is established that the methods have convergence order three. Per iteration the new methods require two function and one first
derivative evaluations. Numerical examples show that the new methods are comparable with the well-known existing methods and give better numerical results in many
aspects. |
| format | Article |
| id | doaj-art-222c6633044d43279fc5aa55186a2b81 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-222c6633044d43279fc5aa55186a2b812025-02-03T01:32:47ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/927450927450Some New Variants of Cauchy's Methods for Solving Nonlinear EquationsTianbao Liu0Hengyan Li1Fundamental Department, Aviation University of Air Force, Changchun 130022, ChinaCollege of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, ChinaWe present and analyze some variants of Cauchy's methods free from second derivative for obtaining simple roots of nonlinear equations. The convergence analysis of the methods is discussed. It is established that the methods have convergence order three. Per iteration the new methods require two function and one first derivative evaluations. Numerical examples show that the new methods are comparable with the well-known existing methods and give better numerical results in many aspects.http://dx.doi.org/10.1155/2012/927450 |
| spellingShingle | Tianbao Liu Hengyan Li Some New Variants of Cauchy's Methods for Solving Nonlinear Equations Journal of Applied Mathematics |
| title | Some New Variants of Cauchy's Methods for Solving Nonlinear Equations |
| title_full | Some New Variants of Cauchy's Methods for Solving Nonlinear Equations |
| title_fullStr | Some New Variants of Cauchy's Methods for Solving Nonlinear Equations |
| title_full_unstemmed | Some New Variants of Cauchy's Methods for Solving Nonlinear Equations |
| title_short | Some New Variants of Cauchy's Methods for Solving Nonlinear Equations |
| title_sort | some new variants of cauchy s methods for solving nonlinear equations |
| url | http://dx.doi.org/10.1155/2012/927450 |
| work_keys_str_mv | AT tianbaoliu somenewvariantsofcauchysmethodsforsolvingnonlinearequations AT hengyanli somenewvariantsofcauchysmethodsforsolvingnonlinearequations |