On a new method for enlarging the radius of convergence for Newton's method
Volume 28 / 2001
Applicationes Mathematicae 28 (2001), 1-15
MSC: 65B05, 47H17, 49D15.
DOI: 10.4064/am28-1-1
Abstract
We provide new local and semilocal convergence results for Newton's method. We introduce Lipschitz-type hypotheses on the $m$th-Frechet derivative. This way we manage to enlarge the radius of convergence of Newton's method. Numerical examples are also provided to show that our results guarantee convergence where others do not.
