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- W2888809335 abstract "For linear inverse problems with a large number of unknown parameters, uncertainty quantification remains a challenging task. In this work, we use Krylov subspace methods to approximate the posterior covariance matrix and describe efficient methods for exploring the posterior distribution. Assuming that Krylov methods (e.g., based on the generalized Golub-Kahan bidiagonalization) have been used to compute an estimate of the solution, we get an approximation of the posterior covariance matrix for `free.' We provide theoretical results that quantify the accuracy of the approximation and of the resulting posterior distribution. Then, we describe efficient methods that use the approximation to compute measures of uncertainty, including the Kullback-Liebler divergence. We present two methods that use preconditioned Lanczos methods to efficiently generate samples from the posterior distribution. Numerical examples from tomography demonstrate the effectiveness of the described approaches." @default.
- W2888809335 created "2018-09-07" @default.
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- W2888809335 date "2018-08-27" @default.
- W2888809335 modified "2023-09-27" @default.
- W2888809335 title "Quantifying uncertainties in Large-scale Bayesian linear inverse problems using Krylov subspace methods" @default.
- W2888809335 hasPublicationYear "2018" @default.
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