一族三阶收敛的Newton型迭代法

A CLASS OF NEWTON-TYPE METHODS WITH THIRD-ORDER CONVERGENCE

基于中点处的导数值构造了一个三阶收敛的Newton型迭代法,与[10]中的方法相比,每步迭代计算相同的函数值,但是数值实例表明该方法的迭代效果更好。此外,在该方法的基础上构造了一族三阶收敛的迭代方法。

Using the first derivative at the midpoint,we present a new modified Newton′s method with third-order convergence,which has better convergence efficiency in some cases than the previous midpoint Newton＇s method .Numerical examples show that the presented method can compete with Newton′s method and other known third-order modifications of Newton′s method.Based on this new method,we obtain a family of Newton-type methods,which also converge cubically.