The Convergence Ball and Error Analysis of the Relaxed Secant Method
A relaxed secant method is proposed. Radius estimate of the convergence ball of the relaxed secant method is attained for the nonlinear equation systems with Lipschitz continuous divided differences of first order. The error estimate is also established with matched convergence order. From the radiu...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/6976205 |
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| _version_ | 1832560823871995904 |
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| author | Rongfei Lin Qingbiao Wu Minhong Chen Lu Liu |
| author_facet | Rongfei Lin Qingbiao Wu Minhong Chen Lu Liu |
| author_sort | Rongfei Lin |
| collection | DOAJ |
| description | A relaxed secant method is proposed. Radius estimate of the convergence ball of the relaxed secant method is attained for the nonlinear equation systems with Lipschitz continuous divided differences of first order. The error estimate is also established with matched convergence order. From the radius and error estimate, the relation between the radius and the speed of convergence is discussed with parameter. At last, some numerical examples are given. |
| format | Article |
| id | doaj-art-ac836c4da4c24d1a93271542749aa7f5 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-ac836c4da4c24d1a93271542749aa7f52025-02-03T01:26:42ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/69762056976205The Convergence Ball and Error Analysis of the Relaxed Secant MethodRongfei Lin0Qingbiao Wu1Minhong Chen2Lu Liu3Department of Mathematics, Taizhou University, Linhai, Zhejiang 317000, ChinaDepartment of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, ChinaDepartment of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310012, ChinaDepartment of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, ChinaA relaxed secant method is proposed. Radius estimate of the convergence ball of the relaxed secant method is attained for the nonlinear equation systems with Lipschitz continuous divided differences of first order. The error estimate is also established with matched convergence order. From the radius and error estimate, the relation between the radius and the speed of convergence is discussed with parameter. At last, some numerical examples are given.http://dx.doi.org/10.1155/2017/6976205 |
| spellingShingle | Rongfei Lin Qingbiao Wu Minhong Chen Lu Liu The Convergence Ball and Error Analysis of the Relaxed Secant Method Advances in Mathematical Physics |
| title | The Convergence Ball and Error Analysis of the Relaxed Secant Method |
| title_full | The Convergence Ball and Error Analysis of the Relaxed Secant Method |
| title_fullStr | The Convergence Ball and Error Analysis of the Relaxed Secant Method |
| title_full_unstemmed | The Convergence Ball and Error Analysis of the Relaxed Secant Method |
| title_short | The Convergence Ball and Error Analysis of the Relaxed Secant Method |
| title_sort | convergence ball and error analysis of the relaxed secant method |
| url | http://dx.doi.org/10.1155/2017/6976205 |
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