| 一类求解非线性方程的3阶收敛迭代格式 |
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| 引用本文： | 开依沙尔·热合曼.一类求解非线性方程的3阶收敛迭代格式[J].江西师范大学学报(自然科学版),2020,44(2):206-208. |
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| 作者姓名： | 开依沙尔·热合曼 |
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| 作者单位： | 1.新疆大学数学与系统科学学院,新疆 乌鲁木齐 830046; 2.新疆大学数学物理研究所,新疆 乌鲁木齐 830046 |
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| 基金项目： | 国家自然科学基金;新疆大学博士启动基金 |
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| 摘 要： | 该文提出了求非线性方程根的3阶收敛的牛顿类迭代方法,并对收敛性进行了证明.该牛顿类迭代方法有效地克服了传统的牛顿迭代方法在目标函数的1阶导数等于0或者接近于0时失效的缺点.通过数值例子来验证该类迭代格式的有效性.
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| 关 键 词： | 非线性方程 牛顿方法 3阶收敛 迭代方法 |
One Class of Third-Order Iteration Methods for Solving Non-Linear Equations |
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| KAYSAR Rahman,' target="_blank" rel="external">.One Class of Third-Order Iteration Methods for Solving Non-Linear Equations[J].Journal of Jiangxi Normal University (Natural Sciences Edition),2020,44(2):206-208. |
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| Authors: | KAYSAR Rahman " target="_blank">' target="_blank" rel="external"> |
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| Institution: | 1.College of Mathematics and System Science,Xinjiang University,Urumqi Xinjiang 830046,China; 2.Institute of Mathematical Physics,Xinjiang University,Urumqi Xinjiang 830046,China |
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| Abstract: | In this paper,one class of modified Newton methods for solving non-linear equations is presented.Analysis of convergence shows that the new method is cubically convergent.The main advantage of this method is that it can overcome the shortcoming of Newton's method which the derivative of the function is either zero or very small of the required root.The effectiveness of the present method is demonstrated by some numerical examples. |
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| Keywords: | nonlinear equations Newton's method third-order convergence iterative methods |
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