Low-rank update of preconditioners for the inexact Newton method with SPD Jacobian

Authors:
L. Bergamaschi;R. Bru;A. MartíNez
Affiliations:
Department of Mathematical Methods and Models for Scientific Applications, University of Padova, Italy;Instituto de Matemática Multidisciplinar, Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Spain;Department of Mathematical Methods and Models for Scientific Applications, University of Padova, Italy
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2011

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Abstract

In this note preconditioners for the Conjugate Gradient method are studied to solve the Newton system with a symmetric positive definite Jacobian. In particular, we define a sequence of preconditioners built by means of BFGS rank-two updates. Reasonable 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 and some numerical results on a number of model problems illustrate the efficiency of the proposed preconditioners.