Steffensen Methods for Solving Generalized Equations

Argyros, Ioannis K., and Hilout, Saïd. "Steffensen Methods for Solving Generalized Equations." Serdica Mathematical Journal 34.2 (2008): 455-466. <http://eudml.org/doc/281512>.

@article{Argyros2008,
abstract = {2000 Mathematics Subject Classification: 65G99, 65K10, 47H04.We provide a local convergence analysis for Steffensen's method in order to solve a generalized equation in a Banach space setting. Using well known fixed point theorems for set-valued maps [13] and Hölder type conditions introduced by us in [2] for nonlinear equations, we obtain the superlinear local convergence of Steffensen's method. Our results compare favorably with related ones obtained in [11].},
author = {Argyros, Ioannis K., Hilout, Saïd},
journal = {Serdica Mathematical Journal},
keywords = {Steffensen's Method; Banach Space; Set-Valued Mapping; Generalized Equations; Aubin Continuity; Divided Difference; Newton's Method; Steffensen's method; Banach space; set-valued mapping; generalized equations; Aubin continuity; divided difference; Newton's method; power series; overconvergence; distribution of the zeroes},
language = {eng},
number = {2},
pages = {455-466},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Steffensen Methods for Solving Generalized Equations},
url = {http://eudml.org/doc/281512},
volume = {34},
year = {2008},
}

TY - JOUR
AU - Argyros, Ioannis K.
AU - Hilout, Saïd
TI - Steffensen Methods for Solving Generalized Equations
JO - Serdica Mathematical Journal
PY - 2008
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 34
IS - 2
SP - 455
EP - 466
AB - 2000 Mathematics Subject Classification: 65G99, 65K10, 47H04.We provide a local convergence analysis for Steffensen's method in order to solve a generalized equation in a Banach space setting. Using well known fixed point theorems for set-valued maps [13] and Hölder type conditions introduced by us in [2] for nonlinear equations, we obtain the superlinear local convergence of Steffensen's method. Our results compare favorably with related ones obtained in [11].
LA - eng
KW - Steffensen's Method; Banach Space; Set-Valued Mapping; Generalized Equations; Aubin Continuity; Divided Difference; Newton's Method; Steffensen's method; Banach space; set-valued mapping; generalized equations; Aubin continuity; divided difference; Newton's method; power series; overconvergence; distribution of the zeroes
UR - http://eudml.org/doc/281512
ER -