On some block diagonal preconditioners using spectral information to accelerate the solution of large linear systems

Séminaire naXys

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 saddle-point (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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