| 解非线性方程的多点曲线法 |
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| 引用本文： | 于桂杰,李维国. 解非线性方程的多点曲线法[J]. 中国石油大学学报(自然科学版), 2009, 33(6) |
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| 作者姓名： | 于桂杰 李维国 |
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| 作者单位： | 1. 中国石油大学,储运与建筑工程学院,山东,青岛,266555
2. 中国石油大学,数学与计算科学学院,山东,东营,257061 |
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| 基金项目： | 国家自然科学基金项目 |
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| 摘 要： | 通过分析常用的求解非线性问题的数值方法,提出一类具强烈几何背景的多点曲线法.多点曲线法不仅具有超二次收敛的特性,而且避免了高阶导数,其收敛域比高阶非Newton法的收敛域有明显改善.数值算例结果表明多点曲线法在奇异非线性方程和非线性方程组求解等问题中非常实用.
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| 关 键 词： | 非线性方程 高阶收敛性 非线性方程组 奇异性 |
Multi-point curve method of solving nonlinear equation |
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| YU Gui-jie,LI Wei-guo. Multi-point curve method of solving nonlinear equation[J]. Journal of China University of Petroleum (Edition of Natural Sciences), 2009, 33(6) |
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| Authors: | YU Gui-jie LI Wei-guo |
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| Abstract: | By analyzing the traditional numerical methods of solving nonlinear equations, a kind of multi-point curve methods which have strong geometric background were presented. This kind of methods not only have super-quadratic convergence, but also can iterate without higher derivatives. Furthermore, the convergent fields of these new methods are obviously improved compared with higher order non-Newton method. The numerical results show that the presented method is effective in solving singular nonlinear equation and nonlinear systems of equations. |
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| Keywords: | nonlinear equation higher order convergence nonlinear systems of equations singularity |
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