牛顿法的收敛性

Convergence of Newton's Method

运用优函数原理，当函数的k-1（k≥2）次导数满足Lipschitz条件时，证明了牛顿法的收敛性。这个结果推广了Kantorovich的经典工作，也包含了Smale的相应工作。

The convergence of Newton's method is verivfied by using the technique of majorizing function under the hypothesis that the (k-1)-th derivative of the function satisfies Lipschitz condition, where k≥22. This result extends the classical work of Kantorovich and contains the corresponding work of smale.