{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T11:11:11Z","timestamp":1680261071076},"reference-count":21,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>An error estimate for the minimal error method for nonlinear ill-posed problems under general a H\u00f6lder-type source condition is not known. We consider a modified minimal error method for nonlinear ill-posed problems. Using a H\u00f6lder-type source condition, we obtain an optimal order error estimate. We also consider the modified minimal error method with noisy data and provide an error estimate.<\/jats:p>","DOI":"10.1515\/cmam-2017-0024","type":"journal-article","created":{"date-parts":[[2017,7,28]],"date-time":"2017-07-28T10:01:43Z","timestamp":1501236103000},"page":"313-321","source":"Crossref","is-referenced-by-count":0,"title":["Modified Minimal Error Method for Nonlinear Ill-Posed Problems"],"prefix":"10.1515","volume":"18","author":[{"given":"M.","family":"Sabari","sequence":"first","affiliation":[{"name":"Department of Mathematical and Computational Sciences , National Institute of Technology Karnataka , Mangaluru 575 025 , India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Santhosh","family":"George","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computational Sciences , National Institute of Technology Karnataka , Mangaluru 575 025 , India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2017,7,28]]},"reference":[{"key":"2023033109580936423_j_cmam-2017-0024_ref_001_w2aab3b7e2578b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"I. K.  Argyros, S.  George and P.  Jidesh,\nInverse free iterative methods for nonlinear ill-posed operator equations,\nInt. J. Math. Math. Sci. 2014 (2014), Article ID 754154.","DOI":"10.1155\/2014\/754154"},{"key":"2023033109580936423_j_cmam-2017-0024_ref_002_w2aab3b7e2578b1b6b1ab2ab2Aa","unstructured":"H. W.  Engl,\nRegularization methods for the stable solution of inverse problems,\nSurveys Math. Indust. 3 (1993), no. 2, 71\u2013143."},{"key":"2023033109580936423_j_cmam-2017-0024_ref_003_w2aab3b7e2578b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"H. W.  Engl, M.  Hanke and A.  Neubauer,\nRegularization of Inverse Problems,\nMath. Appl.,\nKluwer Academic, Dordrecht, 2000.","DOI":"10.1007\/978-94-009-1740-8_3"},{"key":"2023033109580936423_j_cmam-2017-0024_ref_004_w2aab3b7e2578b1b6b1ab2ab4Aa","doi-asserted-by":"crossref","unstructured":"H. W.  Engl, K.  Kunisch and A.  Neubauer,\nConvergence rates for Tikhonov regularisation of nonlinear ill-posed problems,\nInverse Problems 5 (1989), no. 4, 523\u2013540.","DOI":"10.1088\/0266-5611\/5\/4\/007"},{"key":"2023033109580936423_j_cmam-2017-0024_ref_005_w2aab3b7e2578b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"S.  George,\nOn convergence of regularized modified Newton\u2019s method for nonlinear ill-posed problems,\nJ. Inverse Ill-Posed Probl. 18 (2010), 133\u2013146.","DOI":"10.1515\/jiip.2010.004"},{"key":"2023033109580936423_j_cmam-2017-0024_ref_006_w2aab3b7e2578b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"S.  George and M. T.  Nair,\nA modified Newton\u2013Lavrentiev regularization for nonlinear ill-posed Hammerstein-type operator equations,\nJ. Complexity 24 (2008), no. 2, 228\u2013240.","DOI":"10.1016\/j.jco.2007.08.001"},{"key":"2023033109580936423_j_cmam-2017-0024_ref_007_w2aab3b7e2578b1b6b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"S.  George and M. T.  Nair,\nA derivative\u2013free iterative method for nonlinear ill-posed equations with monotone operators,\nJ. Inverse Ill-Posed Probl. (2016), 10.1515\/jiip-2014-0049.","DOI":"10.1515\/jiip-2014-0049"},{"key":"2023033109580936423_j_cmam-2017-0024_ref_008_w2aab3b7e2578b1b6b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"S.  George and M.  Sabari,\nConvergence rate results for steepest descent type method for nonlinear ill-posed equations,\nAppl. Math. Comput. 294 (2017), 169\u2013179.","DOI":"10.1016\/j.amc.2016.09.009"},{"key":"2023033109580936423_j_cmam-2017-0024_ref_009_w2aab3b7e2578b1b6b1ab2ab9Aa","unstructured":"S. F.  Gilyazov,\nIterative solution methods for inconsistent linear equations with non-self-adjoint operators,\nMoscow Univ. Comp. Math. Cyb. 1 (1997), 8\u201313."},{"key":"2023033109580936423_j_cmam-2017-0024_ref_010_w2aab3b7e2578b1b6b1ab2ac10Aa","doi-asserted-by":"crossref","unstructured":"M.  Hanke, A.  Neubauer and O.  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