计算数学
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计算数学  2017, Vol. 39 Issue (1): 14-22    DOI:
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一种求解非线性方程组的3p阶迭代方法
张旭1, 檀结庆2, 艾列富3
1. 合肥工业大学数学学院, 合肥 230009;
2. 安庆师范大学数学与计算科学学院, 安庆 246133;
3. 合肥工业大学数学学院, 合肥 230009
A NEW METHOD WITH CONVERGENCE ORDER 3P FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS
Zhang Xu1, Tan Jieqing2, Ai Liefu3
1. School of Mathematics and Computation Science, Anqing Normal University, Anqing 246133, China;
2. School of Mathematics, Hefei University of Technology, Hefei 230009, China;
3. School of Computer and Information, Anqing Normal University, Anqing 246133, China
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摘要 本文将一种改进的二步迭代算法作为预测,将高斯-勒让德求积公式作为校正,提出了一种求解非线性方程组的具有3p收敛阶的迭代方法.最后给出了一些数值实例,将本文的实验结果与现有的几种迭代方法的实验结果作了比较分析,验证了本文所提出的结果.
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关键词非线性方程组   牛顿迭代   求积公式   效率指数   收敛阶     
Abstract: In this paper,we present a new iterative scheme with the convergence order 3p for solving the systems of nonlinear equations by using a modified two-step iterative algorithm as a predictor and Gauss-Legendre quadrature as a corrector.Numerical examples are given to show that the presented method outperforms the other ones.
Key wordsSystems of nonlinear equations   Newton's method   Quadrature formulas   Efficiency index   Convergence order   
收稿日期: 2015-11-04;
基金资助:

国家自然科学基金项目(61472466,61603003),中央高校基本科研业务费专项经费(JZ2015HGXJ0175)和安徽省自然科学基金(1608085MF144).

引用本文:   
. 一种求解非线性方程组的3p阶迭代方法[J]. 计算数学, 2017, 39(1): 14-22.
. A NEW METHOD WITH CONVERGENCE ORDER 3P FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS[J]. Mathematica Numerica Sinica, 2017, 39(1): 14-22.
 
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