Banach空间中具体三阶收敛的一个修正牛顿法

A modified Newton method with third-order convergence in Banach space

将文献[10]中的一个三阶修正型的牛顿迭代推广到Banach空间中,建立了它的Newton-Kantorovich型收敛性定理并给出了误差估计.最后,用例子说明了定理的应用。

Following the ideas of the Reference [10], we generalize a modified Newton method in Banach space. We establish the Newton-Kantorovich convergence theorem for the modified Newton method in Banach space. We also get the error estimate. Finally, a example is provided to show the application of our theorem.