2020/08/07 by Tim W. Reid, Reid, Tim W., Ilse C. F. Ipsen +5
Decision Sciences · Engineering · Mathematics · #15A06 #15A10 #62F15 #65F10 #65F50 #FOS: Mathematics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Sparse and Compressive Sensing Techniques #Statistical and numerical algorithms
paper · doi:10.48550/arxiv.2008.03225
openalex publication_date 2020/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.