TY - JOUR
T1 - On Newton's Method for Solving Nonlinear Equations and Function Splitting
AU - Ioannis K. Argyros & Saïd Hilout
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 53
EP - 67
PY - 2011
DA - 2011/04
SN - 4
DO - http://doi.org/10.4208/nmtma.2011.m99009
UR - https://global-sci.org/intro/article_detail/nmtma/5958.html
KW - Newton's method, Banach space, majorizing sequence, semilocal convergence, splitting
of an operator.
AB - <p style="text-align: justify;">We provided in [14] and [15] a
semilocal convergence analysis for Newton&#39;s method on a Banach space
setting, by splitting the given operator. In this study, we improve
the error bounds, order of convergence, and simplify the sufficient
convergence conditions. Our results compare favorably with the
Newton-Kantorovich theorem for solving equations.</p>