### Stefania Bellavia (University of Florence, Italy)

#### Inexact Newton methods for systems of nonlinear equations

*Wednesday 6 February 2002 at 15.30, JCMB 6309*

##### Abstract

In this talk we shall consider inexact Newton methods for finding a zero
of F:R^{n}→R^{n}. We will give an overview on these
procedures and we shall focus on Newton-Krylov methods. These latter methods
are variants of inexact Newton methods where the approximate Newton direction
is taken from a subspace of small dimension. the specific Newton-Krylov method
considered here is Newton-GMRES, where the Generalized Minimum RESidual
iterative solver is used to solve the linear system arising at each iteration
of an inexact Newton method

In order to enlarge convergence domain, globally convergent modifications
of the basic Newton-Krylov methods have been considered. Here we will focus
on a hybrid Newton-GMRES method where a global strategy restricted to a
low-dimensional subspace generated by GMRES is performed. This method is an
extension of the classical linesearch Newton-GMRES method and computational
results indicate that it enhances the classical linesearch Newton-GMRES
approach.

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