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On the stopping criterion for numerical methods for linear systems with additive Gaussian noise

Benoît Hamelin, Yves Goussard and Jean-Pierre Dussault

Technical Report (2009)

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Cite this document: Hamelin, B., Goussard, Y. & Dussault, J.-P. (2009). On the stopping criterion for numerical methods for linear systems with additive Gaussian noise (Technical Report n° EPM-RT-2009-10).
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Abstract

We consider the inversion of a linear operator with centered Gaussian white noise by MAP estimation with a Gaussian prior distribution on the solution. The actual estimator is computed approximately by a numerical method. We propose a relation between the stationarity measure of this approximate solution to the mean square error of the exact solution. This relation enables the formulation of a stopping test for the numerical method, met only by iterates that satisfy chosen statistical properties. We extend this development to Gibbs priors using a quadratic extrapolation of the log-likelihood maximized by the MAP estimator.

Open Access document in PolyPublie
Subjects: 2500 Génie électrique et électronique > 2500 Génie électrique et électronique
2500 Génie électrique et électronique > 2514 Traitement des signaux numériques
2950 Mathématiques appliquées > 2960 Modélisation mathématique
Department: Département de génie électrique
Research Center: Non applicable
Date Deposited: 06 Oct 2017 13:51
Last Modified: 24 Oct 2018 16:12
PolyPublie URL: https://publications.polymtl.ca/2649/

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