TY - JOUR
T1 - Ball Convergence for Higher Order Methods Under Weak Conditions
AU - Argyros , Ioannis K.
AU - George , Santhosh
JO - Journal of Mathematical Study
VL - 4
SP - 362
EP - 374
PY - 2015
DA - 2015/12
SN - 48
DO - http://doi.org/10.4208/jms.v48n4.15.04
UR - https://global-sci.org/intro/article_detail/jms/9941.html
KW - Higher order method, Banach space, Fréchet derivative, local convergence.
AB - <p style="text-align: justify;">We present a local convergence analysis for higher order methods in order
to approximate a locally unique solution of an equation in a Banach space setting. In
earlier studies, Taylor expansions and hypotheses on higher order Fréchet-derivatives
are used. We expand the applicability of these methods using only hypotheses on the
first Fréchet derivative. Moreover, we obtain a radius of convergence and computable
error bounds using Lipschitz constants not given before. Numerical examples are also
presented in this study.</p>