Preconditioned iterative methods for linear discrete ill-posed problems from a Bayesian inversion perspective

Authors:
Daniela Calvetti
Affiliations:
Department of Mathematics and Center for Modeling Integrated Metabolic Systems, Case Western Reserve University, Cleveland, OH
Venue:
Journal of Computational and Applied Mathematics - Special issue: Applied computational inverse problems
Year:
2007

Citing 6
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Abstract

In this paper we revisit the solution of ill-posed problems by preconditioned iterative methods from a Bayesian statistical inversion perspective. After a brief review of the most popular Krylov subspace iterative methods for the solution of linear discrete ill-posed problems and some basic statistics results, we analyze the statistical meaning of left and right preconditioners, as well as projected-restarted strategies. Computed examples illustrating the interplay between statistics and preconditioning are also presented.