| 一种新的牛顿迭代在解非线性方程中的应用 |
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| 引用本文： | 刘建平,李霞,马会泉,张瑞丰.一种新的牛顿迭代在解非线性方程中的应用[J].河北科技师范学院学报,2011,25(4):13-16. |
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| 作者姓名： | 刘建平 李霞 马会泉 张瑞丰 |
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| 作者单位： | 河北科技师范学院,河北秦皇岛,066004 |
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| 基金项目： | 秦皇岛市科技局项目(项目编号:201101A430) |
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| 摘 要： | 对牛顿迭代公式进行改进，构造了新的迭代公式，并证明了其在单根附近至少具有二阶收敛性；以按揭贷款问题为算例，在MATLAB7．1软件环境下编程，对简单迭代法、牛顿法、改进的算法进行了计算比较。结果表明，改进的算法不仅比简单迭代法收敛速度快、精度高，而且比牛顿法的精度高。
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| 关 键 词： | 牛顿迭代 非线性方程 收敛阶 按揭贷款 |
The Application of a New Newton Iteration for Nonlinear Equations |
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| LIU Jian-ping,LI Xia,MA Hui-quan,ZHANG Rui-feng.The Application of a New Newton Iteration for Nonlinear Equations[J].Journal of Hebei Normal University of Science & Technology,2011,25(4):13-16. |
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| Authors: | LIU Jian-ping LI Xia MA Hui-quan ZHANG Rui-feng |
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| Institution: | (Hebei Normal University of Science and Technology,Qinhuangdao Hebei,066004,China) |
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| Abstract: | The Newton iterative formula was improved,and a new iterative formula was constructed.It proved that the new iterative formula had at least second order convergence rate at single root.Taking mortgage loans for example,simple iterative method,Newton iterative method and improved method were carried on comparison with calculation in the MATLAB 7.1.The results showed that improved method converged more quickly than simple iterative method,and the method was higher in precision than simple iterative method and Newton method. |
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| Keywords: | Newton iteration nonlinear equations order of convergence mortgage loans |
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