TY - JOUR
T1 - Semilocal Convergence Analysis for MMN-HSS Methods under Hölder Conditions
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 396
EP - 416
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.260416.270217a
UR - https://global-sci.org/intro/article_detail/eajam/10756.html
KW - MMN-HSS method, large sparse systems of nonlinear equation, Hölder conditions, positive-definite Jacobian matrices, semilocal convergence.
AB - <p style="text-align: justify;">Multi-step modified Newton-HSS (MMN-HSS) methods, which are variants
of inexact Newton methods, have been shown to be competitive for solving large sparse
systems of nonlinear equations with positive definite Jacobian matrices. Previously, we
established these MMN-HSS methods under Lipschitz conditions, and we now present a
semilocal convergence theorem assuming the nonlinear operator satisfies milder Hölder
continuity conditions. Some numerical examples demonstrate our theoretical analysis.</p>