Accessibility Of Solutions By Newton's Method

Abstract

We give new conditions for the convergence of Newton's method in Banach spaces, in terms of the degree of logarithmic convexity. These conditions guarantee the convergence of Newton sequence in cases where the hypothesis of Kantorovich theorem are not verified, as we show in some examples.

Keywords:

• Nonlinear equation
• Newton's method
• Fixed Point Principle
• convexity

C.R. Categories:

• 5.1
• 5.15

Classification A.M.S. 1991:

• 47H10
• 47H17
• 65J15