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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