Weaker convergence conditions for the secant method

Ioannis K. Argyros; Saïd Hilout

Applications of Mathematics (2014)

  • Volume: 59, Issue: 3, page 265-284
  • ISSN: 0862-7940

Abstract

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We use tighter majorizing sequences than in earlier studies to provide a semilocal convergence analysis for the secant method. Our sufficient convergence conditions are also weaker. Numerical examples are provided where earlier conditions do not hold but for which the new conditions are satisfied.

How to cite

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Argyros, Ioannis K., and Hilout, Saïd. "Weaker convergence conditions for the secant method." Applications of Mathematics 59.3 (2014): 265-284. <http://eudml.org/doc/261120>.

@article{Argyros2014,
abstract = {We use tighter majorizing sequences than in earlier studies to provide a semilocal convergence analysis for the secant method. Our sufficient convergence conditions are also weaker. Numerical examples are provided where earlier conditions do not hold but for which the new conditions are satisfied.},
author = {Argyros, Ioannis K., Hilout, Saïd},
journal = {Applications of Mathematics},
keywords = {semilocal convergence; secant method; Banach space; majorizing sequence; Hölder condition; divided difference; Fréchet-derivative; semilocal convergence; secant method; Banach space; majorizing sequence; Hölder condition; divided difference; Fréchet-derivative; numerical examples},
language = {eng},
number = {3},
pages = {265-284},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weaker convergence conditions for the secant method},
url = {http://eudml.org/doc/261120},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Argyros, Ioannis K.
AU - Hilout, Saïd
TI - Weaker convergence conditions for the secant method
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 3
SP - 265
EP - 284
AB - We use tighter majorizing sequences than in earlier studies to provide a semilocal convergence analysis for the secant method. Our sufficient convergence conditions are also weaker. Numerical examples are provided where earlier conditions do not hold but for which the new conditions are satisfied.
LA - eng
KW - semilocal convergence; secant method; Banach space; majorizing sequence; Hölder condition; divided difference; Fréchet-derivative; semilocal convergence; secant method; Banach space; majorizing sequence; Hölder condition; divided difference; Fréchet-derivative; numerical examples
UR - http://eudml.org/doc/261120
ER -

References

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