A new semilocal convergence theorem for Newton's method in Banach space using hypotheses on the second Frechet-derivative

作者：Argyros IK^*

来源：Journal of Computational and Applied Mathematics, 2001, 130(1-2): 369-373.

DOI：10.1016/S0377-0427(00)00330-7

• Newton's method
• Banach space
• global convergence
• Frechet-derivative
• Kantorovich hypothesis

A new global Kantorovich-type convergence theorem for Newton's method in Banach space is provided for approximating a solution of a nonlinear equation. It is assumed that a solution exists and the second Frechet-derivative of the operator involved satisfies a Lipschitz condition. Our convergence condition differs from earlier ones, and therefore it has theoretical and practical value. Finally, a simple numerical example is provided to show that our results apply, where earlier ones fail.

• 出版日期2001-5-1