求解区间非线性方程的一类改进算法
A Class of Improved Algorithm for Solving Interval Nonlinear Equation

作者: 邱亮 , 王海军 * , 王琪 :中国矿业大学数学学院,江苏 徐州;

关键词: 含区间参数的区间非线性方程拓展的区间牛顿算法子区间零解区间Interval Nonlinear Equation with Interval Parameters Improved Interval Newton Algorithm Subinterval Interval Zero

摘要: 本文研究了含区间参数的区间非线性方程的求解问题,通过单调分割技术对初始区间进行并行划分,对文献中的拓展区间牛顿算法进行了改进,建立了一类求解区间非线性方程的新算法,给出相关的理论结果并进行数值有效性测试。数值算例表明新算法不仅可以解决拓展区间牛顿法不能解决的问题,并且大大提高了计算效率。

Abstract: In this paper, we consider the problem of solving interval nonlinear equation with interval para-meters. Dividing the initial interval by monotone segment technique, we extended the improved interval Newton algorithm proposed in, and established a class of improved algorithm for solving interval nonlinear equation. Besides, some relevant theoretical results and effectiveness tests are given. Numerical examples show the new algorithm can not only solve problems that can not be solved by improved interval Newton method, but also greatly improve the computational efficiency.

文章引用: 邱亮 , 王海军 , 王琪 (2017) 求解区间非线性方程的一类改进算法。 应用数学进展, 6, 716-725. doi: 10.12677/AAM.2017.65086

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