### Benedetta Morini (University of Florence, Italy)

#### Update preconditioning for sequences of linear systems in optimization

*Wednesday 17 November 2010 at 15.30, JCMB 6206*

##### Abstract

Many problems in science and engineering require the solution of a sequence of
linear systems. Our interest is in the case of large-scale systems solved by
preconditioned Krylov methods. We investigate how to obtain an overall
solution procedure that is cheaper, in terms of total solution costs, than
either reusing the same preconditioner without modifications or recomputing
the preconditioner from scratch for each linear system.

Given a factorized preconditioner for a (reference) matrix of the sequence,
update preconditioning techniques enhance the quality of such preconditioner
through low-cost updates containing information on the subsequent matrices. In
this talk, we propose and analyze preconditioning techniques for sequences of
linear systems arising in optimization. We address the problem of
preconditioning two classes of sequences: sequences of nonsymmetric matrices
arising in Jacobian-free Newton-Krylov methods and sequences of shifted
symmetric and positive definite matrices from trust-region and regularization
procedures.

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