Computational Mathematics and Statistics Seminar By Ilse Ipsen: BayesCG: A Probabilistic Numeric Linear Solver
Professor Ilse Ipsen, Department of Mathematics at North Carolina State University
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 computations.
Computational Mathematics and Statistics Seminar