Geodesic
Local convergence of inexact Newton methods under affine invariant conditions and hypotheses on the second Fréchet derivative
Applicationes Mathematicae, Tome 26 (1999) no. 4, pp. 457-465 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

We use inexact Newton iterates to approximate a solution of a nonlinear equation in a Banach space. Solving a nonlinear equation using Newton iterates at each stage is very expensive in general. That is why we consider inexact Newton methods, where the Newton equations are solved only approximately, and in some unspecified manner. In earlier works [2], [3], natural assumptions under which the forcing sequences are uniformly less than one were given based on the second Fréchet derivative of the operator involved. This approach showed that the upper error bounds on the distances involved are smaller compared with the corresponding ones using hypotheses on the first Fréchet derivative. However, the conditions on the forcing sequences were not given in affine invariant form. The advantages of using conditions given in affine invariant form were explained in [3], [10]. Here we reproduce all the results obtained in [3] but using affine invariant conditions.
DOI : 10.4064/am-26-4-457-465
Keywords: superlinear, Fréchet derivative, weak convergence, inexact Newton method, strong, forcing sequence, Banach space

Ioannis Argyros 1

1 
@article{10_4064_am_26_4_457_465,
     author = {Ioannis Argyros},
     title = {Local convergence of inexact {Newton} methods under affine invariant conditions and hypotheses on the second {Fr\'echet} derivative},
     journal = {Applicationes Mathematicae},
     pages = {457--465},
     year = {1999},
     volume = {26},
     number = {4},
     doi = {10.4064/am-26-4-457-465},
     zbl = {0998.65060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am-26-4-457-465/}
}
TY  - JOUR
AU  - Ioannis Argyros
TI  - Local convergence of inexact Newton methods under affine invariant conditions and hypotheses on the second Fréchet derivative
JO  - Applicationes Mathematicae
PY  - 1999
SP  - 457
EP  - 465
VL  - 26
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am-26-4-457-465/
DO  - 10.4064/am-26-4-457-465
LA  - en
ID  - 10_4064_am_26_4_457_465
ER  - 
%0 Journal Article
%A Ioannis Argyros
%T Local convergence of inexact Newton methods under affine invariant conditions and hypotheses on the second Fréchet derivative
%J Applicationes Mathematicae
%D 1999
%P 457-465
%V 26
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4064/am-26-4-457-465/
%R 10.4064/am-26-4-457-465
%G en
%F 10_4064_am_26_4_457_465
Ioannis Argyros. Local convergence of inexact Newton methods under affine invariant conditions and hypotheses on the second Fréchet derivative. Applicationes Mathematicae, Tome 26 (1999) no. 4, pp. 457-465. doi: 10.4064/am-26-4-457-465

Cité par Sources :