### Luca Bergamaschi, Angeles Martínez (University of Padova, Italy)

#### Quasi-Newton preconditioners for the inexact Newton method

*ERGO Optimization day: Tuesday 7 March 2006 at 14.30, JCMB Lecture Theatre B*

##### Abstract

In this communication preconditioners for solving the linear systems of the
Newton method in each nonlinear iteration are presented. In particular, we
define a sequence of preconditioners built by means of Broyden-type rank-one
updates. Optimality conditions are derived which guarantee that the
preconditioned matrices are not far from the identity in a matrix norm. Some
notes on the implementation of the corresponding inexact Newton method are
given. Sequential and parallel numerical results on two model problems
illustrate the effectiveness of the proposed approach in the preconditioning
of BiCGstab iterative method.

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