{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T10:39:38Z","timestamp":1766486378159},"reference-count":24,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we consider a simplified iteratively regularized Gauss\u2013Newton method in a Banach space setting under a general source condition. We will obtain order-optimal error estimates both for an a priori stopping rule and for a Morozov-type stopping rule together with a posteriori choice of the regularization parameter. An advantage of a general source condition is that it provides a unified setting for the error analysis which can be applied to the cases of both severely and mildly ill-posed problems. We will give a numerical example of a parameter identification problem to discuss the performance of the method.<\/jats:p>","DOI":"10.1515\/cmam-2018-0165","type":"journal-article","created":{"date-parts":[[2020,5,26]],"date-time":"2020-05-26T14:28:18Z","timestamp":1590503298000},"page":"321-341","source":"Crossref","is-referenced-by-count":7,"title":["Simplified Iteratively Regularized Gauss\u2013Newton Method in Banach Spaces Under a General Source Condition"],"prefix":"10.1515","volume":"20","author":[{"given":"Pallavi","family":"Mahale","sequence":"first","affiliation":[{"name":"Department of Mathematics , Visvesvaraya National Institute of Technology , Nagpur , Nagpur-440010, Maharashtra , India"}]},{"given":"Sharad Kumar","family":"Dixit","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Visvesvaraya National Institute of Technology , Nagpur , Nagpur-440010, Maharashtra , India"}]}],"member":"374","published-online":{"date-parts":[[2019,3,8]]},"reference":[{"key":"2023033110443937138_j_cmam-2018-0165_ref_001_w2aab3b7d942b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"M.  Burger and B.  Kaltenbacher,\nRegularizing Newton\u2013Kaczmarz methods for nonlinear ill-posed problems,\nSIAM J. Numer. Anal. 44 (2006), no. 1, 153\u2013182.","DOI":"10.1137\/040613779"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_002_w2aab3b7d942b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"M.  Hanke, A.  Neubauer and O.  Scherzer,\nA convergence analysis of the Landweber iteration for nonlinear ill-posed problems,\nNumer. Math. 72 (1995), no. 1, 21\u201337.","DOI":"10.1007\/s002110050158"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_003_w2aab3b7d942b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"T.  Hein and B.  Hofmann,\nApproximate source conditions for nonlinear ill-posed problems\u2014chances and limitations,\nInverse Problems 25 (2009), no. 3, Article ID 035003.","DOI":"10.1088\/0266-5611\/25\/3\/035003"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_004_w2aab3b7d942b1b6b1ab2ab4Aa","doi-asserted-by":"crossref","unstructured":"B.  Hofmann,\nApproximate source conditions in Tikhonov\u2013Phillips regularization and consequences for inverse problems with multiplication operators,\nMath. Methods Appl. Sci. 29 (2006), no. 3, 351\u2013371.","DOI":"10.1002\/mma.686"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_005_w2aab3b7d942b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"T.  Hohage,\nLogarithmic convergence rates of the iteratively regularized Gauss\u2013Newton method for an inverse potential and an inverse scattering problem,\nInverse Problems 13 (1997), no. 5, 1279\u20131299.","DOI":"10.1088\/0266-5611\/13\/5\/012"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_006_w2aab3b7d942b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"T.  Hohage,\nRegularization of exponentially ill-posed problems,\nNumer. Funct. Anal. Optim. 21 (2000), no. 3\u20134, 439\u2013464.","DOI":"10.1080\/01630560008816965"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_007_w2aab3b7d942b1b6b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"Q.  Jin and L.  Stals,\nNonstationary iterated Tikhonov regularization for ill-posed problems in Banach spaces,\nInverse Problems 28 (2012), no. 10, Article ID 104011.","DOI":"10.1088\/0266-5611\/28\/10\/104011"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_008_w2aab3b7d942b1b6b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"Q.  Jin and M.  Zhong,\nOn the iteratively regularized Gauss\u2013Newton method in Banach spaces with applications to parameter identification problems,\nNumer. Math. 124 (2013), no. 4, 647\u2013683.","DOI":"10.1007\/s00211-013-0529-5"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_009_w2aab3b7d942b1b6b1ab2ab9Aa","doi-asserted-by":"crossref","unstructured":"Q.  Jin and M.  Zhong,\nNonstationary iterated Tikhonov regularization in Banach spaces with uniformly convex penalty terms,\nNumer. Math. 127 (2014), no. 3, 485\u2013513.","DOI":"10.1007\/s00211-013-0594-9"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_010_w2aab3b7d942b1b6b1ab2ac10Aa","doi-asserted-by":"crossref","unstructured":"B.  Kaltenbacher,\nA posteriori parameter choice strategies for some Newton type methods for the regularization of nonlinear ill-posed problems,\nNumer. Math. 79 (1998), no. 4, 501\u2013528.","DOI":"10.1007\/s002110050349"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_011_w2aab3b7d942b1b6b1ab2ac11Aa","doi-asserted-by":"crossref","unstructured":"B.  Kaltenbacher,\nA note on logarithmic convergence rates for nonlinear Tikhonov regularization,\nJ. Inverse Ill-Posed Probl. 16 (2008), no. 1, 79\u201388.","DOI":"10.1515\/jiip.2008.006"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_012_w2aab3b7d942b1b6b1ab2ac12Aa","doi-asserted-by":"crossref","unstructured":"B.  Kaltenbacher and B.  Hofmann,\nConvergence rates for the iteratively regularized Gauss\u2013Newton method in Banach spaces,\nInverse Problems 26 (2010), no. 3, Article ID 035007.","DOI":"10.1088\/0266-5611\/26\/3\/035007"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_013_w2aab3b7d942b1b6b1ab2ac13Aa","doi-asserted-by":"crossref","unstructured":"B.  Kaltenbacher, A.  Neubauer and O.  Scherzer,\nIterative Regularization Methods for Nonlinear Ill-posed Problems,\nRadon Ser. Comput. Appl. Math. 6,\nWalter de Gruyter, Berlin, 2008.","DOI":"10.1515\/9783110208276"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_014_w2aab3b7d942b1b6b1ab2ac14Aa","doi-asserted-by":"crossref","unstructured":"B.  Kaltenbacher, F.  Sch\u00f6pfer and T.  Schuster,\nIterative methods for nonlinear ill-posed problems in Banach spaces: Convergence and applications to parameter identification problems,\nInverse Problems 25 (2009), no. 6, Article ID 065003.","DOI":"10.1088\/0266-5611\/25\/6\/065003"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_015_w2aab3b7d942b1b6b1ab2ac15Aa","doi-asserted-by":"crossref","unstructured":"S.  Langer and T.  Hohage,\nConvergence analysis of an inexact iteratively regularized Gauss\u2013Newton method under general source conditions,\nJ. Inverse Ill-Posed Probl. 15 (2007), no. 3, 311\u2013327.","DOI":"10.1515\/jiip.2007.017"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_016_w2aab3b7d942b1b6b1ab2ac16Aa","doi-asserted-by":"crossref","unstructured":"P.  Mahale,\nSimplified generalized Gauss\u2013Newton iterative method under Morozove type stopping rule,\nNumer. Funct. Anal. Optim. 36 (2015), no. 11, 1448\u20131470.","DOI":"10.1080\/01630563.2015.1067822"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_017_w2aab3b7d942b1b6b1ab2ac17Aa","doi-asserted-by":"crossref","unstructured":"P.  Mahale and S. K.  Dixit,\nConvergence analysis of simplified iteratively regularized Gauss\u2013Newton method in a Banach space setting,\nAppl. Anal. 97 (2018), no. 15, 2686\u20132719.","DOI":"10.1080\/00036811.2017.1386785"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_018_w2aab3b7d942b1b6b1ab2ac18Aa","doi-asserted-by":"crossref","unstructured":"P.  Mahale and S. K.  Dixit,\nError estimates for the simplified iteratively regularized Gauss\u2013Newton method in Banach spaces under a Morozov-type stopping rule,\nJ. Inverse Ill-Posed Probl. 26 (2018), no. 3, 311\u2013333.","DOI":"10.1515\/jiip-2017-0059"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_019_w2aab3b7d942b1b6b1ab2ac19Aa","doi-asserted-by":"crossref","unstructured":"P.  Mahale and M. T.  Nair,\nA simplified generalized Gauss\u2013Newton method for nonlinear ill-posed problems,\nMath. Comp. 78 (2009), no. 265, 171\u2013184.","DOI":"10.1090\/S0025-5718-08-02149-2"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_020_w2aab3b7d942b1b6b1ab2ac20Aa","doi-asserted-by":"crossref","unstructured":"F.  Margotti,\nMixed gradient-Tikhonov methods for solving nonlinear ill-posed problems in Banach spaces,\nInverse Problems 32 (2016), no. 12, Article ID 125012.","DOI":"10.1088\/0266-5611\/32\/12\/125012"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_021_w2aab3b7d942b1b6b1ab2ac21Aa","doi-asserted-by":"crossref","unstructured":"S.  Pereverzev and E.  Schock,\nMorozov\u2019s discrepancy principle for Tikhonov regularization of severely ill-posed problems in finite-dimensional subspaces,\nNumer. Funct. Anal. Optim. 21 (2000), no. 7\u20138, 901\u2013916.","DOI":"10.1080\/01630560008816993"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_022_w2aab3b7d942b1b6b1ab2ac22Aa","unstructured":"W.  Sun and Y.-X.  Yuan,\nOptimization Theory and Methods. Nonlinear Programming,\nSpringer Optim. Appl. 1,\nSpringer, New York, 2006."},{"key":"2023033110443937138_j_cmam-2018-0165_ref_023_w2aab3b7d942b1b6b1ab2ac23Aa","doi-asserted-by":"crossref","unstructured":"U.  Tautenhahn,\nOn a general regularization scheme for nonlinear ill-posed problems,\nInverse Problems 13 (1997), no. 5, 1427\u20131437.","DOI":"10.1088\/0266-5611\/13\/5\/020"},{"key":"2023033110443937138_j_cmam-2018-0165_ref_024_w2aab3b7d942b1b6b1ab2ac24Aa","doi-asserted-by":"crossref","unstructured":"C.  Z\u00e1linscu,\nConvex Analysis in General Vector Spaces,\nWorld Scientific, River Edge, 2002.","DOI":"10.1142\/5021"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/20\/2\/article-p321.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0165\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0165\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T12:56:01Z","timestamp":1680267361000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0165\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,8]]},"references-count":24,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,8,14]]},"published-print":{"date-parts":[[2020,4,1]]}},"alternative-id":["10.1515\/cmam-2018-0165"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2018-0165","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2019,3,8]]}}}