On the Stopping Criterion for Numerical Methods Used to Solve Linear Systems with Additive Gaussian Noise

Benoit Hamelin (benoit-2.hamelinpolymtl.ca)
Yves Goussard (yves.goussardpolymtl.ca)
Jean-Pierre Dussault (jean-pierre.dussaultusherbrooke.ca)

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.

Keywords: Least Squares, Regularization, Gibbs Prior, MAP, Stopping condition

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Applications -- Science and Engineering (Statistics )

Citation: Rapport technique EPM-RT-2009-10 de l'École Polytechnique de Montréal, Montréal, Canada, september 2009

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Entry Submitted: 09/21/2009
Entry Accepted: 09/21/2009
Entry Last Modified: 12/04/2009

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