| 对牛顿类方法的讨论 |
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| 引用本文： | 李海合,何万生. 对牛顿类方法的讨论[J]. 甘肃科学学报, 2012, 0(1): 20-22 |
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| 作者姓名： | 李海合 何万生 |
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| 作者单位： | 兰州交通大学数理与软件工程学院;天水师范学院数学与统计学院 |
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| 摘 要： | 对解非线性和超越方程f（x）=0的＂牛顿类＂方法xn＋1=xn-f（xn）/（αf（xn）＋f′（xn））作了进一步的分析,认为参数α的取值范围直接影响公式的收敛速度,从而给出了α取值的依赖性条件,并给出了加速算法和数值算例.
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| 关 键 词： | 牛顿类方法 迭代公式 收敛速度 |
Study on Newton-like Method |
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| LI Hai-he,HE Wan-sheng. Study on Newton-like Method[J]. Journal of Gansu Sciences, 2012, 0(1): 20-22 |
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| Authors: | LI Hai-he HE Wan-sheng |
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| Affiliation: | 1.School of Mathematics,Physics and Software Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China; 2.School of Mathematics and Statistics,Tianshui Normal College,Tianshui 741001,China) |
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| Abstract: | For the "Newton-like" method xn+1=xn-f(xn)/(αf(xn)+f′(xn)) of solving nonlinear and transcendental equation f(x)=0,a further analysis is proposed in this paper.The analysis indicates that the range of parameter α directly affects the convergence rate of the formula.Hence,the dependent conditions of α are given here.The accelerated algorithm and the numerical examples are also presented. |
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| Keywords: | Newton-like method iterative formula convergence rate |
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