Probabilistic Linear Solvers

Jon Cockayne, University of Warwick, UK - 11:15

A fundamental task in numerical computation is the solution of large linear systems, and iterative methods are among the most widely used solvers for sparse linear systems. However, for more challenging systems a substantial error can be present even after many iterations have been performed. This talk will introduce probabilistic linear solvers, a class of linear solvers in which the output is a probability measure rather than a point estimate of the solution, designed to quantify the remaining error. Several approaches will be explored, including recent Bayesian linear solvers such as the Bayesian Conjugate Gradient Method. New, non-Bayesian solvers will also be introduced, and criteria by which their output can be interpreted will be discussed.

Invited by Jana de Wiljes