关于牛顿迭代法中导数离散格式的探讨  

Derivatives Discretization in Newtonian Iteration Method

作　　者：李义强 袁占斌[1] 张念 LI Yiqiang;YUAN Zhanbin;ZHANG Nian(School of Mathematics and Statistics,Northwestern Polytechnical University,Xi'an 710072,China)

机构地区：[1]西北工业大学数学与统计学院,陕西西安710072

出　　处：《高等数学研究》2024年第4期14-16,共3页Studies in College Mathematics

基　　金：西北工业大学玛丽学院课程思政建设项目.

摘　　要：基于导数的不同形式对牛顿迭代法中的导数进行离散,分别推导出弦截法和Steffensen迭代法,从而揭示了三种迭代法之间的关系.然后通过比较这两种方法中对导数值的近似精度,发现Steffensen方法对导数的近似结果更好,从而能保证该方法比弦截法收敛更快.By discretizing the derivatives term in Newton's iteration method,we derive the chord intercept method and Steffensen iteration method,revealing the relationship between these three iteration methods.Comparing the approximation accuracy of derivative values,we find that the Steffensen method provides better approximations,ensuring it converges more quickly than the chord intercept method.

关 键 词：NEWTON迭代法 弦截法 Steffensen迭代法 

分 类 号：O172.2[理学—数学]