| 求解方程的一类迭代公式 |
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| 引用本文： | 李声锋,檀结庆,谢进,霍星.求解方程的一类迭代公式[J].数学研究及应用,2010,30(2):217-226. |
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| 作者姓名： | 李声锋 檀结庆 谢进 霍星 |
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| 作者单位： | 合肥工业大学计算机与信息学院, 安徽 合肥 230009; 合肥工业大学应用数学研究所, 安徽 合肥 230009; 蚌埠学院理学系, 安徽 蚌埠 233000;;合肥工业大学计算机与信息学院, 安徽 合肥 230009; 合肥工业大学应用数学研究所, 安徽 合肥 230009;合肥工业大学计算机与信息学院, 安徽 合肥 230009; 合肥工业大学应用数学研究所, 安徽 合肥 230009; 合肥学院数学与物理系, 安徽 合肥 230601;合肥工业大学计算机与信息学院, 安徽 合肥 230009; 合肥工业大学应用数学研究所, 安徽 合肥 230009 |
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| 基金项目： | 国家自然科学基金项目(Grant Nos.60773043;60473114), 教育部科学技术研究重大项目(Grant No.309017),教育部博士点基金项目(Grant No.20070359014),安徽省教育厅自然研究重点项目(Grant No.KJ2010A237),安徽省教育厅科技创新团队基金(Grant No.2005TD03),安徽省高校省级优秀青年人才基金项目(Grant No.2010SQRL118),安徽省高校青年教师科研资助项目(Grant No.2008jq1158). |
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| 摘 要： | Using the forms of Newton iterative function, the iterative function of Newton's method to handle the problem of multiple roots and the Halley iterative function, we give a class of iterative formulae for solving equations in one variable in this paper and show that their convergence order is at least quadratic. At last we employ our methods to solve some non-linear equations and compare them with Newton's method and Halley's method. Numerical results show that our iteration schemes are convergent if we choose two suitable parametric functions λ(x) and μ(x). Therefore, our iteration schemes are feasible and effective.
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| 关 键 词： | 迭代公式 解方程 迭代函数 牛顿方法 非线性方程 数值结果 参数函数 收敛阶 |
| 收稿时间： | 1/1/2009 12:00:00 AM |
| 修稿时间： | 2009/5/20 0:00:00 |
A Class of Iterative Formulae for Solving Equations |
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| Sheng Feng LI,Jie Qing TAN,Jin XIE and Xing HUO.A Class of Iterative Formulae for Solving Equations[J].Journal of Mathematical Research with Applications,2010,30(2):217-226. |
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| Authors: | Sheng Feng LI Jie Qing TAN Jin XIE and Xing HUO |
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| Institution: | 1. School of Computer & Information,Hefei University of Technology,Anhui 230009,P.R.China; Institute of Applied Mathematics,Hefei University of Technology,Anhui 230009,P.R.China; Department of Mathematic
2. School of Computer & Information,Hefei University of Technology,Anhui 230009,P.R.China; Institute of Applied Mathematics,Hefei University of Technology,Anhui 230009,P.R.China |
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| Abstract: | Using the forms of Newton iterative function, the iterative function of Newton's method to handle the problem of multiple roots and the Halley iterative function, we give a class of iterative formulae for solving equations in one variable in this paper and show that their convergence order is at least quadratic. At last we employ our methods to solve some non-linear equations and compare them with Newton's method and Halley's method. Numerical results show that our iteration schemes are convergent if we choose two suitable parametric functions $\lambda (x)$ and $\mu (x)$. Therefore, our iteration schemes are feasible and effective. |
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| Keywords: | Non-linear equation iterative function order of convergence Newton's method Halley's method |
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