BayesCG as an uncertainty aware version of CG
BayesCG as an uncertainty aware version of CG
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. We present a CG-based implementation of BayesCG with a structure-exploiting prior distribution. The BayesCG output consists of CG iterates and posterior covariances that can be propagated to subsequent computations. The covariances are low-rank and maintained in factored form. This allows easy generation of accurate samples to probe uncertainty in subsequent computations. Numerical experiments confirm the effectiveness of the posteriors and their low-rank approximations.
Reid, Tim W.
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Ipsen, Ilse C.F.
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Cockayne, Jonathan
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Oates, Chris J.
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Reid, Tim W.
8ab4ae9b-b21e-4fa4-ba9c-8a4bf9bc7cc9
Ipsen, Ilse C.F.
83eae4c2-19d4-4f74-9d16-4146a63d2c4c
Cockayne, Jonathan
da87c8b2-fafb-4856-938d-50be8f0e4a5b
Oates, Chris J.
3af13c56-dc47-4d2c-867f-e4e933e74619
Reid, Tim W., Ipsen, Ilse C.F., Cockayne, Jonathan and Oates, Chris J.
(2020)
BayesCG as an uncertainty aware version of CG.
Pre-print.
Abstract
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. We present a CG-based implementation of BayesCG with a structure-exploiting prior distribution. The BayesCG output consists of CG iterates and posterior covariances that can be propagated to subsequent computations. The covariances are low-rank and maintained in factored form. This allows easy generation of accurate samples to probe uncertainty in subsequent computations. Numerical experiments confirm the effectiveness of the posteriors and their low-rank approximations.
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BayesCG As An Uncertainty Aware Version of CG
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Accepted/In Press date: 7 August 2020
e-pub ahead of print date: 7 August 2020
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Local EPrints ID: 451749
URI: http://eprints.soton.ac.uk/id/eprint/451749
PURE UUID: febedf9a-27a1-403e-9ab5-d5c8415c0be4
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Date deposited: 25 Oct 2021 16:31
Last modified: 17 Mar 2024 04:09
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Contributors
Author:
Tim W. Reid
Author:
Ilse C.F. Ipsen
Author:
Chris J. Oates
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