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
Conjugate gradient regularization under general smoothness and noise assumptions
We study noisy linear operator equations in Hilbert space under a self-adjoint operator. Approximate solutions are sought by conjugate gradient type iteration, given as Krylov-subspace minimizers under a general weight function. Solution smoothness is given in terms of general source conditions. The noise may be controlled in stronger norm. We establish conditions under which stopping according to a modified discrepancy principle yields optimal regularization of the iteration. The present analysis extends much of the known theory and reveals some intrinsic features which are hidden when studying standard conjugate gradient type regularization under standard smoothness assumptions. In particular, under a non-self adjoint operator, regularization of the associated normal equation is a direct consequence from the main result and does not require a separate treatment.
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