关于牛顿迭代法中导数离散格式的探讨

Derivatives Discretization in Newtonian Iteration Method

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.