| 非线性方程求根的高阶迭代方法 |
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| 引用本文： | 倪克琳,李宝毅.非线性方程求根的高阶迭代方法[J].天津师范大学学报(自然科学版),2012,32(2):32-37. |
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| 作者姓名： | 倪克琳 李宝毅 |
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| 作者单位： | 天津师范大学数学科学学院,天津,300387 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 通过对已有误差方程进行加权组合,消去较低阶数,得到了3个新的带参数四阶收敛迭代公式和1个新的五阶收敛迭代公式,收敛效率分别达到了1.587和1.495,并证明了这些公式的局部高阶收敛性.最后通过数值算例验证了这些方法的有效性.
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| 关 键 词： | 非线性方程 Newton法 迭代方法 四阶收敛 五阶收敛 |
High-order iterative method for searching root of nonlinear equation |
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| NI Ke-lin
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LI Bao-yi.High-order iterative method for searching root of nonlinear equation[J].Journal of Tianjin Normal University(Natural Science Edition),2012,32(2):32-37. |
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| Authors: | NI Ke-lin LI Bao-yi |
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| Institution: | College of Mathematical Science,Tianjin Normal University,Tianjin 300387,Chin |
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| Abstract: | Three new fourth order convergent iteration formulas with parameters and a new five order convergent iteration formula are obtained by using the weighted combination of existing error equations and eliminating the lower order terms,and their convergence efficiencies reach to 1.587 and 1.495 respectively.The local high order convergences of the formulas are determined,and the effectiveness of these methods are verified by using numerical examples. |
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| Keywords: | nonlinear equation Newton method iterative method fourth order convergence five order convergence |
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