caa a22 4500 606244719 CHVBK 20210128101331.0 cr unu---uuuuu 210128e20150501xx s 000 0 eng 10.1007/s12044-015-0226-7 doi (NATIONALLICENCE)springer-10.1007/s12044-015-0226-7 NAIR M. Department of Mathematics, Indian Institute of Technology Madras, 600 036, Chennai, India aut Morozov-type discrepancy principle for nonlinear ill-posed problems under η -condition [Elektronische Daten] [M NAIR] For proving the existence of a regularization parameter under a Morozov-type discrepancy principle for Tikhonov regularization of nonlinear ill-posed problems, it is required to impose additional nonlinearity assumptions on the forward operator. Lipschitz continuity of the Freéchet derivative and requirement of the Lipschitz constant to depend on a source condition is one such restriction (Ramlau P, Numer. Funct. Anal. Optim. 23(1&22) (2003) 147-172). Another nonlinearity condition considered by Scherzer (Computing, 51 (1993 ) 45-60) was by requiring the forward operator to be close to a linear operator in a restricted sense. A seemingly natural nonlinear assumption which appears in many applications which attracted attention in various contexts of the study of nonlinear problems is the so-called η-condition. However, a Morozov-type discrepancy principle together with η-condition does not seem to have been studied, except in a recent paper by the author (Bull. Aust. Math. Soc. 79 (2009) 337-342), where error estimates under a general source condition is derived, by assuming the existence of the parameter. In this paper, the existence of the parameter satisfying a Morozov-type discrepancy principle is proved under the η-condition on the forward operator, by assuming the source condition as in the papers of Scherzer (Computing, 51 (1993) 45-60) and Ramlau (Numer. Funct. Anal. Optim. 23(1&22) (2003) 147-172). This source condition is, in fact, a special case of the source condition in the author's paper (Bull. Aust. Math. Soc. 79 (2009) 337-342). Indian Academy of Sciences, 2015 Tikhonov regularization nationallicence nonlinear ill-posed problems nationallicence discrepancy principle nationallicence η -condition nationallicence Proceedings - Mathematical Sciences Springer India 125/2(2015-05-01), 227-238 0253-4142 125:2<227 2015 125 12044 https://doi.org/10.1007/s12044-015-0226-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s12044-015-0226-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- NAIR M. Department of Mathematics, Indian Institute of Technology Madras, 600 036, Chennai, India aut NATIONALLICENCE 773 0- Proceedings - Mathematical Sciences Springer India 125/2(2015-05-01), 227-238 0253-4142 125:2<227 2015 125 12044