BayesCG: A probabilistic numeric linear solver

We present the probabilistic numeric solver BayesCG, for solving linear systems with real symmetric positive definite coefficient matrices. BayesCG is an uncertainty aware extension of the conjugate gradient (CG) method that performs solution-based inference with Gaussian distributions to capture the uncertainty in the solution due to early termination. Under a structure exploiting `Krylov' prior, BayesCG produces the same iterates as CG. The Krylov posterior covariances have low rank, and are maintained in factored form to preserve symmetry and positive semi-definiteness. This allows efficient generation of accurate samples to probe uncertainty in subsequent computation.

Speaker bio: Ilse C.F. Ipsen received a BS from the University of Kaiserslautern in Germany and a Ph.D. from Penn State, both in Computer Science. She is a Professor of Mathematics at NCState, with affiliate appointments in Statistics and the Institute for Advanced Analytics. Her research interests include numerical linear algebra, randomized algorithms, and probabilistic numerics. She is a Fellow of the AAAS and SIAM.