Papers › BayesCG As An Uncertainty Aware Version of CG

BayesCG As An Uncertainty Aware Version of CG

7 Aug 2020arXiv:2008.03225links table onlyarchive 2025-07-28

Tim W. Reid, Ilse C. F. Ipsen, Jon Cockayne, Chris J. Oates

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The Bayesian Conjugate Gradient method (BayesCG) is a probabilistic generalization of the Conjugate Gradient method (CG) for solving linear systems with real symmetric positive definite coefficient matrices. Our CG-based implementation of BayesCG under a structure-exploiting prior distribution represents an 'uncertainty-aware' version of CG. Its output consists of CG iterates and posterior covariances that can be propagated to subsequent computations. The covariances have low-rank and are maintained in factored form. This allows easy generation of accurate samples to probe uncertainty in downstream computations. Numerical experiments confirm the effectiveness of the low-rank posterior covariances.

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