Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
IMPACT FACTOR increased in 2015: 0.987
Rank 59 out of 312 in category Mathematics and 93 out of 254 in Applied Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition
SCImago Journal Rank (SJR) 2015: 0.583
Source Normalized Impact per Paper (SNIP) 2015: 1.106
Impact per Publication (IPP) 2015: 0.712
Mathematical Citation Quotient (MCQ) 2015: 0.43
On the choice of the regularization parameter in ill-posed problems with approximately given noise level of data
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.
Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.