Seminario di Calcolo Numerico e Calcolo delle probabilità (Aula 1B1)
D. Calvetti, E. Somersalo (Case Western Reserve University, USA)
Bayes meets Krylov: preconditioning under determined linear systems
The solution of linear inverse problems when the number of unknown parameters outnumbers the number of data requires handling a nontrivial null space. By restating the problem within the Bayesian framework, a priori information about the unknown can be utilized for enrich the solution with contributions from the null space. In particular, if a Krylov subspace iterative linear solver is used, the additional information can be encoded in the form of a right preconditioned. In this talk we analyze how the right preconditioned changes the Krylov subspaces where the iterates live, and draw a tighter connection between Bayesian inference and Krylov subspace methods. The performance of this Krylov-meets-Bayes approach is illustrated with a few computed examples.