| 一个三阶牛顿变形方法 |
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| 引用本文： | 王霞,张银银.一个三阶牛顿变形方法[J].数学的实践与认识,2009,39(14). |
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| 作者姓名： | 王霞 张银银 |
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| 作者单位： | 1. 郑州轻工业学院,数学与信息科学系,河南,郑州,450002
2. 华中科技大学,数学系,湖北,武汉,430074 |
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| 基金项目： | 河南省教委自然科学基金，河南省教育厅自然科学基金 |
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| 摘 要： | 基于反函数建立的积分方程,结合Simpson公式,给出了一个非线性方程求根的新方法,即为牛顿变形方法.证明了它至少三次收敛到单根,与牛顿法相比,提高了收敛阶和效率指数.文末给出数值试验,且与牛顿法和同类型牛顿变形法做了比较.结果表明方法具有较好的优越性,它丰富了非线性方程求根的方法.
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| 关 键 词： | 牛顿迭代法 收敛阶 收敛效率 数值试验 |
A Third-order Variant of Newton's Method |
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| WANG Xia,ZHANG Yin-yin.A Third-order Variant of Newton's Method[J].Mathematics in Practice and Theory,2009,39(14). |
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| Authors: | WANG Xia ZHANG Yin-yin |
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| Abstract: | Based on inverse function′s integral equation and Simpson scheme,a new method for solving roots of non-linear equations is obtained,which is a variant of Newton′s method.The present method is proved to be at least third-order convergence near simple root and it improves convergence order and efficiency index compared with Newton′s method.In the end,numerical tests are given and compared with Newton′s method and Newton-like methods.The results show that the present method has some more advantages than others.It enriches the methods for solving the roots of non-linear equations. |
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| Keywords: | newton iteration method efficiency index convergence order numerical test |
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