| Article ID: | iaor2013600 |
| Volume: | 62 |
| Issue: | 1 |
| Start Page Number: | 115 |
| End Page Number: | 132 |
| Publication Date: | Jan 2013 |
| Journal: | Numerical Algorithms |
| Authors: | Hilout Sad, Argyros Ioannis |
| Keywords: | Newton method, Banach space |
We present new sufficient conditions for the semilocal convergence of Newton’s method to a locally unique solution of an equation in a Banach space setting. Upper bounds on the limit points of majorizing sequences are also given. Numerical examples are provided, where our new results compare favorably to earlier ones such as Argyros 2004), Argyros and Hilout (2006, 2010, 2011), Ortega and Rheinboldt (1970) and Potra and Pták (1984).