Convergence domains under Zabrejko–Zinčenko conditions using recurrent functions
Volume 38 / 2011
Applicationes Mathematicae 38 (2011), 193-209
MSC: 65G99, 65H10, 65B05, 65N30, 47H17, 49M15.
DOI: 10.4064/am38-2-5
Abstract
We provide a semilocal convergence analysis for Newton-type methods using our idea of recurrent functions in a Banach space setting. We use Zabrejko–Zinčenko conditions. In particular, we show that the convergence domains given before can be extended under the same computational cost. Numerical examples are also provided to show that we can solve equations in cases not covered before.
