Local convergence of a one parameter fourth-order Jarratt-type method in Banach spaces

I. K. Argyros; D. González; S. K. Khattri

Commentationes Mathematicae Universitatis Carolinae (2016)

  • Volume: 57, Issue: 3, page 289-300
  • ISSN: 0010-2628

Abstract

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We present a local convergence analysis of a one parameter Jarratt-type method. We use this method to approximate a solution of an equation in a Banach space setting. The semilocal convergence of this method was recently carried out in earlier studies under stronger hypotheses. Numerical examples are given where earlier results such as in [Ezquerro J.A., Hernández M.A., New iterations of R -order four with reduced computational cost, BIT Numer. Math. 49 (2009), 325–342] cannot be used to solve equations but our results can be applied.

How to cite

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Argyros, I. K., González, D., and Khattri, S. K.. "Local convergence of a one parameter fourth-order Jarratt-type method in Banach spaces." Commentationes Mathematicae Universitatis Carolinae 57.3 (2016): 289-300. <http://eudml.org/doc/286813>.

@article{Argyros2016,
abstract = {We present a local convergence analysis of a one parameter Jarratt-type method. We use this method to approximate a solution of an equation in a Banach space setting. The semilocal convergence of this method was recently carried out in earlier studies under stronger hypotheses. Numerical examples are given where earlier results such as in [Ezquerro J.A., Hernández M.A., New iterations of $R$-order four with reduced computational cost, BIT Numer. Math. 49 (2009), 325–342] cannot be used to solve equations but our results can be applied.},
author = {Argyros, I. K., González, D., Khattri, S. K.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Banach space; Newton's method; local convergence; radius of convergence},
language = {eng},
number = {3},
pages = {289-300},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Local convergence of a one parameter fourth-order Jarratt-type method in Banach spaces},
url = {http://eudml.org/doc/286813},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Argyros, I. K.
AU - González, D.
AU - Khattri, S. K.
TI - Local convergence of a one parameter fourth-order Jarratt-type method in Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 3
SP - 289
EP - 300
AB - We present a local convergence analysis of a one parameter Jarratt-type method. We use this method to approximate a solution of an equation in a Banach space setting. The semilocal convergence of this method was recently carried out in earlier studies under stronger hypotheses. Numerical examples are given where earlier results such as in [Ezquerro J.A., Hernández M.A., New iterations of $R$-order four with reduced computational cost, BIT Numer. Math. 49 (2009), 325–342] cannot be used to solve equations but our results can be applied.
LA - eng
KW - Banach space; Newton's method; local convergence; radius of convergence
UR - http://eudml.org/doc/286813
ER -

References

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