| 一族带有个参数的三阶收敛迭代方法 |
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| 引用本文： | 刘天宝,王彩玲,马明娟,左平. 一族带有个参数的三阶收敛迭代方法[J]. 吉林大学学报(理学版), 2012, 50(4): 711-714 |
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| 作者姓名： | 刘天宝 王彩玲 马明娟 左平 |
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| 作者单位： | 1. 空军航空大学 数学教研室, 长春 130022,2. 吉林大学 数学学院, 长春 130012 |
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| 基金项目： | 教育部博士点新教师基金 |
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| 摘 要： | 提出一种求解非线性方程f(x)=0近似解问题的一族带有3个参数的迭代方法, 通过选取不同的参数值, 可以得到不同的迭代方法. 该方法不用计算函数的二阶导数即可达到三阶收敛. 收敛性分析和数值实验表明, 该方法与其他同阶收敛性质方法相比具有一定的有效性.
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| 关 键 词： | 非线性方程 迭代方法 收敛阶 牛顿方法 |
A Family of Three-Parameter Third-Order Convergence Iteration Method for Solving Nonlinear Equations |
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| LIU Tian-bao , WANG Cai-ling , MA Ming-juan , ZUO Ping. A Family of Three-Parameter Third-Order Convergence Iteration Method for Solving Nonlinear Equations[J]. Journal of Jilin University: Sci Ed, 2012, 50(4): 711-714 |
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| Authors: | LIU Tian-bao WANG Cai-ling MA Ming-juan ZUO Ping |
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| Affiliation: | 1. Teaching and Research Section of Mathematics, Aviation University of Air Force, Changchun 130022, China;
2. College of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | We first presented a family of three-parameter third-order convergence iteration method for solving nonlinear equations and obtained different iteration methods by taking different values of the parameters.We then proveed that the iteration methods have third-order convergence similar to those of existing methods,our methods also avoid computing the second derivative.Finally,we tested the methods on several numerical examples and illustrated that our methods are competitive with several other methods. |
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| Keywords: | nonlinear equation iteration methods convergence of order Newton’s method |
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