Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
Increased IMPACT FACTOR 2013: 0.593
Rank 143 out of 299 in category Mathematics in the 2013 Thomson Reuters Journal Citation Report/Science Edition
SCImago Journal Rank (SJR): 0.466
Source Normalized Impact per Paper (SNIP): 1.251
Mathematical Citation Quotient 2013: 0.51
Volume 22 (2014)
Volume 21 (2013)
Volume 20 (2012)
Volume 19 (2011)
Volume 18 (2011)
Volume 17 (2009)
Volume 16 (2008)
Volume 15 (2007)
Volume 14 (2006)
Volume 13 (2005)
Volume 12 (2004)
Volume 11 (2003)
Volume 10 (2002)
Volume 9 (2001)
Volume 8 (2000)
Volume 7 (1999)
Volume 6 (1998)
Volume 5 (1997)
Volume 4 (1996)
Volume 3 (1995)
Volume 2 (1994)
Most Downloaded Articles
- Chemnitz Symposium on Inverse ProblemsChemnitz, Germany, September 27–28, 2007 by Hofmann, B.
- Obituary of Alfredo Lorenzi
- A numerical study of heuristic parameter choice rules for total variation regularization by Kindermann, Stefan/ Mutimbu, Lawrence D. and Resmerita, Elena
- Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems by Klibanov, Michael V.
- Minisymposium — Recent progress in regularization theory by Neubauer, A.
Conjugate gradient regularization under general smoothness and noise assumptions
1Universität Potsdam, Institut für Mathematik, Am Neuen Palais 10, 14469 Potsdam, Germany.
2Weierstraß Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin, Germany.
Citation Information: Journal of Inverse and Ill-posed Problems. Volume 18, Issue 6, Pages 701–726, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2010.033, December 2010
- Published Online:
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.