对牛顿迭代法的改进  

Improvement on Newton iteration method

作　　者：王乐成 赫亚兰 韩新丽 李小花 卢凤兰 马秋菊 杨录峰 WANG Lecheng;HE Yalan;HAN Xinli;LI Xiaohua;LU Fenglan;MA Qiuju;YANG Lufeng(School of Mathematics and Information Science,North Minzu University,Yinchuan 750021,China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021

出　　处：《高师理科学刊》2020年第3期23-26,共4页Journal of Science of Teachers＇College and University

摘　　要：通过了解牛顿法及其它牛顿法的改进方法,总结了牛顿法及其收敛性质,对牛顿法的优缺点进行了简要概括.对非线性超越方程f(x)=0的牛顿法的迭代次数进行了改进,得到修正的算术平均牛顿法.通过数值实验,将修正的算术平均牛顿法的迭代次数和迭代速度与其它牛顿法做比较.结果表明,经过改进的算术平均牛顿法是有效的.By understanding the Newton′s method and other improved Newton′s methods,summarizes the Newton method and its convergence properties,and briefly summarizes the advantages and disadvantages of Newton method.The number of iterations of Newton′s method for nonlinear transcendental equation f(x)=0 is improved,and the modified arithmetic mean Newton′s method is obtained.Through numerical experiments,the number and speed of iterations of the modified arithmetic mean Newton′s method are compared with other Newton′s methods.The results show that the improved arithmetic mean Newton′s method is effective.

关 键 词：牛顿迭代法 二阶收敛性 收敛速度 

分 类 号：O241.7[理学—计算数学]