A new semilocal convergence theorem for Newton's method involving twice Frechet-differentiability at only one point

作者：Hu ZY^*

来源：Journal of Computational and Applied Mathematics, 2005, 181(2): 321-325.

DOI：10.1016/j.cam.2004.12.005

• Newton's method
• Frechet-differentiability
• error estimates
• convergence

In this study, we provide a new semilocal convergence theorem for Newton's method. It is assumed that an operator is twice continuously Frechet-differentiable at only one point. Finally, a simple numerical example is given to show that our results can apply, but earlier similar ones fail.

• 出版日期2005-9-15