Local convergence theorems of Newton’s method for nonlinear equations using outer or generalized inverses

Ioannis K. Argyros

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 3, page 603-614
  • ISSN: 0011-4642

Abstract

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We provide local convergence theorems for Newton’s method in Banach space using outer or generalized inverses. In contrast to earlier results we use hypotheses on the second instead of the first Fréchet-derivative. This way our convergence balls differ from earlier ones. In fact we show that with a simple numerical example that our convergence ball contains earlier ones. This way we have a wider choice of initial guesses than before. Our results can be used to solve undetermined systems, nonlinear least squares problems and ill-posed nonlinear operator equations.

How to cite

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Argyros, Ioannis K.. "Local convergence theorems of Newton’s method for nonlinear equations using outer or generalized inverses." Czechoslovak Mathematical Journal 50.3 (2000): 603-614. <http://eudml.org/doc/30587>.

@article{Argyros2000,
abstract = {We provide local convergence theorems for Newton’s method in Banach space using outer or generalized inverses. In contrast to earlier results we use hypotheses on the second instead of the first Fréchet-derivative. This way our convergence balls differ from earlier ones. In fact we show that with a simple numerical example that our convergence ball contains earlier ones. This way we have a wider choice of initial guesses than before. Our results can be used to solve undetermined systems, nonlinear least squares problems and ill-posed nonlinear operator equations.},
author = {Argyros, Ioannis K.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Newton’s method; Banach space; Fréchet-derivative; local convergence; outer inverse; generalized inverse; Newton's method; Banach space; Fréchet-derivative; local convergence; outer inverse; generalized inverse},
language = {eng},
number = {3},
pages = {603-614},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Local convergence theorems of Newton’s method for nonlinear equations using outer or generalized inverses},
url = {http://eudml.org/doc/30587},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Argyros, Ioannis K.
TI - Local convergence theorems of Newton’s method for nonlinear equations using outer or generalized inverses
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 3
SP - 603
EP - 614
AB - We provide local convergence theorems for Newton’s method in Banach space using outer or generalized inverses. In contrast to earlier results we use hypotheses on the second instead of the first Fréchet-derivative. This way our convergence balls differ from earlier ones. In fact we show that with a simple numerical example that our convergence ball contains earlier ones. This way we have a wider choice of initial guesses than before. Our results can be used to solve undetermined systems, nonlinear least squares problems and ill-posed nonlinear operator equations.
LA - eng
KW - Newton’s method; Banach space; Fréchet-derivative; local convergence; outer inverse; generalized inverse; Newton's method; Banach space; Fréchet-derivative; local convergence; outer inverse; generalized inverse
UR - http://eudml.org/doc/30587
ER -

References

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