| 一种适合于迭代求复数根的抛物牛顿法 |
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| 引用本文： | 王礼广,熊岳山,蔡放.一种适合于迭代求复数根的抛物牛顿法[J].湖南师范大学自然科学学报,2007,30(4):11-14. |
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| 作者姓名： | 王礼广 熊岳山 蔡放 |
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| 作者单位： | 1. 国防科技大学理学院,中国,长沙,410073;南华大学数理学院,中国,衡阳,421001
2. 国防科技大学理学院,中国,长沙,410073 |
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| 基金项目： | 国家自然科学基金资助项目(60773022)，湖南省教育厅科研资助项目(06C712) |
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| 摘 要： | 提出了一种适合于迭代求复数根的抛物牛顿法,并进行了收敛性分析,给出了若干数值实例.该方法与切线牛顿法共同构架了复数域上求非线性代数方程近似解的基本方法,在切线牛顿法失效时它可替代使用.其收敛的阶为3,高于切线牛顿法的收敛阶2.特别地,对于实多项式可迭代求出全部的实根和复根.与已有的抛物迭代法相比较,该方法是单步而非多步.
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| 关 键 词： | 非线性方程求根法 迭代法 牛顿法 多项式根 |
| 文章编号： | 1000-2537（2007）04-0011-04 |
| 收稿时间： | 2007-04-03 |
| 修稿时间： | 2007年4月3日 |
A Parabolic Newton Method Fitting for Iterative Finding Complex Roots |
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| WANG Li-guang,XIONG Yue-shan,CAI Fang.A Parabolic Newton Method Fitting for Iterative Finding Complex Roots[J].Journal of Natural Science of Hunan Normal University,2007,30(4):11-14. |
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| Authors: | WANG Li-guang XIONG Yue-shan CAI Fang |
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| Institution: | 1. School of Sience, National University of Defense Technology, Changsha 410073, China 2. School of Mathematics and Physics,Nanhua University, Hengyang 421001 ,China |
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| Abstract: | A parabolic Newton method fitting for iterative finding complex roots is proposed.The analysis for it's convergence is put up,and some actual examples are shown.This method and the tangent Newton method together construct the basic idea to find approximate roots of nolinear algebraic equation in the complex number field,and it can take place of the tangent Newton method when the later is failed.It's convergence order is at least 3,which is greater than 2 in the tangent Newton method.Specially,all the real and complex roots of a real polynomial can be calculated by this method.It is a single-step but not muti-step method compared with known parabolic iterative methods. |
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| Keywords: | finding roots of non-linear equations iteration method Newton method roots of polynomials |
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