| 解非线性方程的免导数牛顿算法 |
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| 引用本文： | 李万斌,颜永明.解非线性方程的免导数牛顿算法[J].怀化学院学报,2010,29(5):34-37. |
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| 作者姓名： | 李万斌 颜永明 |
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| 作者单位： | 1. 南京市,第十四中学,江苏,南京,210031
2. 湖南科技大学,数学与计算科学学院,湖南,湘潭,411201 |
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| 摘 要： | 通过函数值的运算近似牛顿法中的导数项,构造了一个免导数的牛顿法.该算法与牛顿法一样,具有二阶收敛速度,但不需要用到函数的导数.通过与二分法结合,实现该算法的全局收敛性.数值结果表明该算法是有效的.
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| 关 键 词： | 非线性方程 免导数 区间二分法 二阶收敛 |
A Gradient-free Newton Method for Nonlinear Equation |
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| LI Wan-bin,YAN Yong-ming.A Gradient-free Newton Method for Nonlinear Equation[J].Journal of Huaihua University,2010,29(5):34-37. |
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| Authors: | LI Wan-bin YAN Yong-ming |
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| Abstract: | This paper first proposed a gradient-free method for nonlinear equation by approximating the derivative term in the Newton method.Like the Newton method,the algorithm is convergent two-order.Moreover,a globally convergent derivative-free method was presented by combining the above gradient-free method with the bisection method.Some numerical results show that the algorithm is effective. |
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| Keywords: | nonlinear equation derivative-free interval bisection method square convergence |
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