| 关于Newton迭代公式的几个改进 |
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| 引用本文： | 郑华盛,刘永生. 关于Newton迭代公式的几个改进[J]. 南昌航空工业学院学报, 2006, 20(3): 1-4 |
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| 作者姓名： | 郑华盛 刘永生 |
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| 作者单位： | 南昌航空工业学院 江西南昌330063 |
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| 基金项目： | 江西省教育厅高校教学改革研究课题 |
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| 摘 要： | 通过对Newton迭代公式进行改进,本文构造了三种新的迭代公式。迭代公式I是一种单步迭代公式,在单根附近具有二阶收敛速度,且无须求函数的导数值;迭代公式II也是一种单步迭代公式,在单根附近具有三阶收敛速度;迭代公式III是一种两步迭代公式,具有至少三阶收敛速度,虽然该公式形式比较复杂,但是具有计算时不需求函数的导数值的优点。此外,证明了三种新的迭代公式的收敛性。最后,通过数值实验验证了三种迭代公式的有效性。
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| 关 键 词： | Newton迭代公式 迭代函数 收敛阶 |
| 文章编号： | 1001-4926(2006)03-0001-04 |
| 收稿时间： | 2006-08-08 |
| 修稿时间： | 2006-08-08 |
Several variations of Newton iteration method |
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| ZHENG Hua-sheng,LIU Yong-sheng. Several variations of Newton iteration method[J]. Journal of Nanchang Institute of Aeronautical Technology(Natural Science Edition), 2006, 20(3): 1-4 |
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| Authors: | ZHENG Hua-sheng LIU Yong-sheng |
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| Affiliation: | Nanchang Institute of Aeronautical Technology, Nanchang, Jiangxi 330063 China |
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| Abstract: | Based on Newton iterative method,three new kinds of iterative methods are constructed in this paper.The first iterative formula(I) is a one-step iterative formula.It has second order convergence rate at single root,and needn't evaluate derivative of function.The second iterative formula(II) is also one-step iterative formula and has three order convergence at single root.The third iterative formula(III) is a two-step iterative formula.There is at least three order convergence rate.Although iterative formula(III) is complex,it has advantage of free-computing derivative of function.Moreover,the convergence of three kinds of methods is proved.Finally,some numerical experiments are given,and numerical results are satisfied. |
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| Keywords: | Newton iterative formula iterative function order of convergence |
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