| 求解非线性方程七阶收敛的牛顿迭代修正格式 |
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| 引用本文： | 王晓峰,石东洋.求解非线性方程七阶收敛的牛顿迭代修正格式[J].数学杂志,2015,35(5):1017-1025. |
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| 作者姓名： | 王晓峰 石东洋 |
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| 作者单位： | 郑州大学数学与统计学院, 河南 郑州 450001;河南科技学院数学科学学院, 河南 新乡 453003,郑州大学数学与统计学院, 河南 郑州 450001 |
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| 基金项目： | Supported by National Natural Science Foundation of China (U1304106) |
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| 摘 要： | 本文研究了非线性方程求解的问题.利用泰勒公式和耦合方法,获得了一种求解非线性方程的加速收敛的七阶迭代改进格式,该格式不需要计算高阶导数,且具有更大的收敛半径,大大提高了计算效率.
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| 关 键 词： | 迭代法 非线性方程 扩展指数 效率指数 收敛半径 |
| 收稿时间： | 2013/4/17 0:00:00 |
| 修稿时间： | 2014/7/31 0:00:00 |
A NOVEL AND PRECISE SEVENTH-ORDER NEWTON'S ITERATIVE METHOD FOR SOLVING NONLINEAR EQUATIONS |
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| WANG Xiao-feng and SHI Dong-yang.A NOVEL AND PRECISE SEVENTH-ORDER NEWTON''S ITERATIVE METHOD FOR SOLVING NONLINEAR EQUATIONS[J].Journal of Mathematics,2015,35(5):1017-1025. |
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| Authors: | WANG Xiao-feng and SHI Dong-yang |
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| Institution: | School of Math. and Statistics, Zhengzhou University, Zhengzhou 450001, China;Department of Math., Henan Institute of Science and Technology, Xinxiang 453003, China and School of Math. and Statistics, Zhengzhou University, Zhengzhou 450001, China |
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| Abstract: | In this paper, we study the problem of solving nonlinear equations. By using Taylor formulas and cupling method, we get a novel and robust three-step seventh-order iterative scheme. The contributed without memory method does not need to calculate higher order derivatives and has a large radius of convergence and higher efficiency of calculation. |
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| Keywords: | iterative method nonlinear equations extended computational index efficiency index convergence radius |
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