On the discrepancy principle

2003/04/17 by A. G. Ramm
Physics and Astronomy · Mathematics · #math-ph #math.MP #msc:34R30 #msc:35R25 #msc:35R30 #msc:37C35 #msc:37L05 #msc:37N30 #msc:47A52 #msc:47J06 #msc:65M30 #msc:65N21

paper · pdf

published as NFAA, 8, N2, (2003)

arxiv created 2003/04/17 · arxiv updated 2009/11/30

Abstract

A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy principle, in general, does not yield uniform with respect to the data convergence. An a priori choice of the regularization parameter is proposed and justified for some nonlinear operator equations.

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