求非线性方程重根的区间算法
Interval Algorithm of Nonlinear Equation with Multiple Root
DOI: 10.12677/AAM.2018.78119, PDF,    科研立项经费支持
作者: 武松, 肖旺, 王海军：中国矿业大学数学学院，江苏 徐州；王奕为：中国矿业大学附属中学，江苏 徐州
关键词: 非线性方程；重根；区间迭代法；区间Newton法；收敛性；Nonlinear Equation； Multiple Root； Interval Iterative Method； Interval Newton Method； Convergence
摘要: 本文主要研究非线性方程重根问题的求解方法。基于区间分析理论和函数的二阶近似逼近，设计了一种求解非线性方程重根问题的新方法，并进行了相关的收敛性分析，给出了近似解在数值上的误差估计，最后通过数值算例与传统的区间迭代法进行了对比。新方法不仅能解决非线性方程的单根问题，而且能有效解决非线性方程的二重根问题，且计算量较小，收敛速度较快，数值结果有效可靠。
Abstract: This article mainly discusses methods for solving nonlinear equation. Based on theory of interval analysis and the second order approximate approach, a new method is proposed to solve nonlinear equation with multiple root, carrying related convergence analysis, giving numerical error estimation of approximate solution, contract with traditional method though several numerical examples at last. It can not only solve nonlinear equation with simple root but also solve nonlinear equation with double root efficiently. At the same time, the new method needs less amount of computation and has fast convergence; the numerical results are effective and reliable.
文章引用：武松, 王奕为, 肖旺, 王海军. 求非线性方程重根的区间算法[J]. 应用数学进展, 2018, 7(8): 1020-1027. https://doi.org/10.12677/AAM.2018.78119

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