Computational Mathematics and Statistics Seminar By Ilse Ipsen: BayesCG: A Probabilistic Numeric Linear Solver
Speaker:
Professor Ilse Ipsen, Department of Mathematics at North Carolina State University
Title:
BayesCG: A probabilistic numeric linear solver
Abstract:
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 for the efficient generation of accurate samples to probe uncertainty in subsequent computations.
Computational Mathematics and Statistics Seminar
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