We consider regularization of linear ill-posed problems *Au* = ƒ in Hilbert spaces. Approximations *u*
_{r} to the solution *u*
_{*} can be constructed by the Tikhonov method or by the Lavrentiev method, by iterative or by other methods. We assume that instead of ƒ ∈ *R*(*A*) noisy data are available with the approximately given noise level *δ*: in process *δ* → 0 it holds || − ƒ||/*δ* ≤ *c* with unknown constant *c*. We propose a new a-posteriori rule for the choice of the regularization parameter *r* = *r*(*δ*) guaranteeing *u*
_{r(δ)} → *u*
_{*} for *δ* → 0. Note that such convergence is not guaranteed for the parameter choice given by the L-curve rule, by the GCV-rule, by the quasioptimality criterion and also for discrepancy principle ||*Au*
_{r} − || = *bδ* with *b* < *c*. The error estimates are given, which in case || − ƒ|| ≤ *δ* are quasioptimal and order-optimal.

# Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Get Access to Full Text# On the choice of the regularization parameter in ill-posed problems with approximately given noise level of data

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Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 14, Issue 3, Pages 251–266, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939406777340928,

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