Silvia Gazzola (Università di Pisa)
Abstract: Inverse problems broadly consist in recovering the causes of some observed and measured effects, and arise in many applications, such as imaging (e.g., computed tomography). Inverse problems are inherently ill-posed: even in a discrete linear setting (the one mainly adopted in this talk), regularization is pivotal in achieving meaningful solutions. This talk focuses on iterative regularization methods, mainly based on Krylov projection methods. Special emphasis is given on the so-called `hybrid projection' methods, i.e., regularization methods that combine projection onto suitable (Krylov) solution subspaces and variational regularization methods (such as Tikhonov). These solvers, when based on some standard Krylov methods, are well-established for regularizing linear inverse problems and allow adaptive choice of the regularization parameter(s). This talk will also present some novel randomized iterative solvers, which may provide (even) more efficient alternatives to their standard counterparts.
Afterwards there will be a tea and coffee break
To introduce PhD students and postdocs to the topic of the institute's colloquium there will be a talk "What is ... a Krylov subspace?" at 1:00 p.m. in room 1.22.
If you want to join the institute's colloquium online, please ask Lisa Franz for the Zoom meeting details.
