On a secant-like method for solving generalized equations

Ioannis K. Argyros; Said Hilout

Mathematica Bohemica (2008)

  • Volume: 133, Issue: 3, page 313-320
  • ISSN: 0862-7959

Abstract

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In the paper by Hilout and Piétrus (2006) a semilocal convergence analysis was given for the secant-like method to solve generalized equations using Hölder-type conditions introduced by the first author (for nonlinear equations). Here, we show that this convergence analysis can be refined under weaker hypothesis, and less computational cost. Moreover finer error estimates on the distances involved and a larger radius of convergence are obtained.

How to cite

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Argyros, Ioannis K., and Hilout, Said. "On a secant-like method for solving generalized equations." Mathematica Bohemica 133.3 (2008): 313-320. <http://eudml.org/doc/250543>.

@article{Argyros2008,
abstract = {In the paper by Hilout and Piétrus (2006) a semilocal convergence analysis was given for the secant-like method to solve generalized equations using Hölder-type conditions introduced by the first author (for nonlinear equations). Here, we show that this convergence analysis can be refined under weaker hypothesis, and less computational cost. Moreover finer error estimates on the distances involved and a larger radius of convergence are obtained.},
author = {Argyros, Ioannis K., Hilout, Said},
journal = {Mathematica Bohemica},
keywords = {secant-like method; generalized equations; Aubin continuity; radius of convergence; divided difference; secant-like method; generalized equations; Aubin continuity; radius of convergence; divided difference; error estimates},
language = {eng},
number = {3},
pages = {313-320},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a secant-like method for solving generalized equations},
url = {http://eudml.org/doc/250543},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Argyros, Ioannis K.
AU - Hilout, Said
TI - On a secant-like method for solving generalized equations
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 3
SP - 313
EP - 320
AB - In the paper by Hilout and Piétrus (2006) a semilocal convergence analysis was given for the secant-like method to solve generalized equations using Hölder-type conditions introduced by the first author (for nonlinear equations). Here, we show that this convergence analysis can be refined under weaker hypothesis, and less computational cost. Moreover finer error estimates on the distances involved and a larger radius of convergence are obtained.
LA - eng
KW - secant-like method; generalized equations; Aubin continuity; radius of convergence; divided difference; secant-like method; generalized equations; Aubin continuity; radius of convergence; divided difference; error estimates
UR - http://eudml.org/doc/250543
ER -

References

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