Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems
In this work, two multi-step derivative-free iterative methods are presented for solving system of nonlinear equations. The new methods have high computational efficiency and low computational cost. The order of convergence of the new methods is proved by a development of an inverse first-order divi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-02-01
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| Series: | Algorithms |
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| Online Access: | http://www.mdpi.com/1999-4893/9/1/14 |
| _version_ | 1818273613286998016 |
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| author | Xiaofeng Wang Xiaodong Fan |
| author_facet | Xiaofeng Wang Xiaodong Fan |
| author_sort | Xiaofeng Wang |
| collection | DOAJ |
| description | In this work, two multi-step derivative-free iterative methods are presented for solving system of nonlinear equations. The new methods have high computational efficiency and low computational cost. The order of convergence of the new methods is proved by a development of an inverse first-order divided difference operator. The computational efficiency is compared with the existing methods. Numerical experiments support the theoretical results. Experimental results show that the new methods remarkably reduce the computing time in the process of high-precision computing. |
| first_indexed | 2024-12-12T22:00:45Z |
| format | Article |
| id | doaj.art-203f18da1ba5478d99b36d9265685742 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-12-12T22:00:45Z |
| publishDate | 2016-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-203f18da1ba5478d99b36d92656857422022-12-22T00:10:31ZengMDPI AGAlgorithms1999-48932016-02-01911410.3390/a9010014a9010014Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear SystemsXiaofeng Wang0Xiaodong Fan1School of Mathematics and Physics, Bohai University, Jinzhou 121013, ChinaSchool of Mathematics and Physics, Bohai University, Jinzhou 121013, ChinaIn this work, two multi-step derivative-free iterative methods are presented for solving system of nonlinear equations. The new methods have high computational efficiency and low computational cost. The order of convergence of the new methods is proved by a development of an inverse first-order divided difference operator. The computational efficiency is compared with the existing methods. Numerical experiments support the theoretical results. Experimental results show that the new methods remarkably reduce the computing time in the process of high-precision computing.http://www.mdpi.com/1999-4893/9/1/14system of nonlinear equationsderivative-free iterative methodsorder of convergencehigh precision |
| spellingShingle | Xiaofeng Wang Xiaodong Fan Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems Algorithms system of nonlinear equations derivative-free iterative methods order of convergence high precision |
| title | Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems |
| title_full | Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems |
| title_fullStr | Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems |
| title_full_unstemmed | Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems |
| title_short | Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems |
| title_sort | two efficient derivative free iterative methods for solving nonlinear systems |
| topic | system of nonlinear equations derivative-free iterative methods order of convergence high precision |
| url | http://www.mdpi.com/1999-4893/9/1/14 |
| work_keys_str_mv | AT xiaofengwang twoefficientderivativefreeiterativemethodsforsolvingnonlinearsystems AT xiaodongfan twoefficientderivativefreeiterativemethodsforsolvingnonlinearsystems |