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| 用于求根问题的一个基于Thiele连分式的四阶收敛的迭代方法 | |
| 引用本文： | 李声锋. 用于求根问题的一个基于Thiele连分式的四阶收敛的迭代方法[J]. 数学研究及应用, 2019, 39(1): 10-22 |
| 作者姓名： | 李声锋 |
| 作者单位： | 蚌埠学院应用数学研究所, 安徽 蚌埠 233030 |
| 基金项目： | 国家自然科学基金(Grant No.11571071),安徽省教育厅自然科学研究重点项目(Grant No.KJ2013A183),安徽省教育厅优秀人才项目(Grant No.gxfxZD2016270),蚌埠学院国家级科研基金培育项目(Grant No.2018GJPY04). |
| 摘 要： | In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele's continued fraction. Analysis of convergence shows that the order of convergence of the introduced iterative method for a simple root is four. To illustrate the efficiency and performance of the proposed method we give some numerical examples. |
| 关 键 词： | NON-LINEAR equation Thiele’s continued FRACTION Viscovatov algorithm iterative method order of convergence |
| 收稿时间： | 2018-04-04 |
| 修稿时间： | 2018-08-12 |
A Fourth-Order Convergent Iterative Method by Means of Thiele's Continued Fraction for Root-Finding Problem |
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| Shengfeng LI. A Fourth-Order Convergent Iterative Method by Means of Thiele's Continued Fraction for Root-Finding Problem[J]. Journal of Mathematical Research with Applications, 2019, 39(1): 10-22 | |
| Authors: | Shengfeng LI |
| Abstract: | In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele's continued fraction. Analysis of convergence shows that the order of convergence of the introduced iterative method for a simple root is four. To illustrate the efficiency and performance of the proposed method we give some numerical examples. |
| Keywords: | non-linear equation Thiele''s continued fraction Viscovatov algorithm iterative method order of convergence |
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