On some block diagonal preconditioners using spectral information to accelerate the solution of large linear systems
Séminaire naXys
Date : 25/11/2014 13:00  25/11/2014 14:00
Lieu : E25  Salle de conférence du département de mathématique
Orateur(s) : Charlotte Tannier (naXys, University of Namur)
Organisateur(s) : Timoteo Carletti
Optimization problems with constraints arise in many areas of the
sciences and engineering. In this context, the (possibly very large)
linear systems which need to be solved in sequence have a saddlepoint
(or KKT) form. These systems are generally symmetric and indefinite,
such that standard Krylov subspace methods like MINRES are applicable.
To accelerate the convergence of such iterative schemes, preconditioning
techniques are usually considered, that improve the condition number
and/or the eigenvalues clustering of the underlying matrices. In this
talk, we consider the « ideal » block diagonal preconditioner proposed
by Murphy, Golub and Wathen (2000) and based on the exact Schur
complement, and focus on the case where the (1,1) block has few very
small eigenvalues. Assuming that a good approximation of these
eigenvalues and their associated eigenvectors is available, we propose
different approximations of the block diagonal preconditioner of Murphy,
Golub and Wathen, analyze the spectral properties of the preconditioned
matrices and illustrate the performance of the proposed preconditioners
through some numerical illustrations.
Contact :
Timoteo Carletti

49 03

timoteo.carletti@unamur.be
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