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

Title:

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

Creator:

Argyros, Ioannis K.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:32b4c765-4d0d-436c-bd36-173c0d951dd6
uuid:32b4c765-4d0d-436c-bd36-173c0d951dd6

Subject:

Newton’s method, Banach space, Fréchet-derivative, local convergence, outer inverse, and generalized inverse

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

603-613

Source:

Czechoslovak Mathematical Journal | 2000 Volume:50 | Number:3

Harvested from:

CDK

Metadata only:

false