{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T14:24:47Z","timestamp":1762352687268,"version":"3.40.5"},"reference-count":32,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we deal with nonlinear ill-posed operator equations involving a monotone operator in the setting of Hilbert scales. Our convergence analysis of the proposed derivative-free method is based on the simple property of the norm of a self-adjoint operator. Using a general H\u00f6lder-type source condition, we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) for choosing the regularization parameter. Finally, we applied the proposed method to the parameter identification problem in an elliptic PDE in the setting of Hilbert scales and compare the results with the corresponding method in Hilbert space.<\/jats:p>","DOI":"10.1515\/cmam-2018-0019","type":"journal-article","created":{"date-parts":[[2018,7,12]],"date-time":"2018-07-12T16:46:34Z","timestamp":1531413994000},"page":"765-778","source":"Crossref","is-referenced-by-count":5,"title":["Derivative Free Regularization Method for Nonlinear Ill-Posed Equations in Hilbert Scales"],"prefix":"10.1515","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3530-5539","authenticated-orcid":false,"given":"Santhosh","family":"George","sequence":"first","affiliation":[{"name":"Department of Mathematical and Computational Sciences , National Institute of Technology Karnataka , Mangaluru -575 025 , India"}]},{"given":"K.","family":"Kanagaraj","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computational Sciences , National Institute of Technology Karnataka , Mangaluru -575 025 , India"}]}],"member":"374","published-online":{"date-parts":[[2018,7,7]]},"reference":[{"key":"2023033110105325051_j_cmam-2018-0019_ref_001_w2aab3b7e2132b1b6b1ab2ab1Aa","unstructured":"J. I.  Al\u2019ber,\nThe solution by the regularization method of operator equations of the first kind with accretive operators in a Banach space,\nDiffer. Uravn. 11 (1975), no. 12, 2242\u20132248, 2302."},{"key":"2023033110105325051_j_cmam-2018-0019_ref_002_w2aab3b7e2132b1b6b1ab2ab2Aa","unstructured":"Y.  Alber and I.  Ryazantseva,\nNonlinear Ill-Posed Problems of Monotone Type,\nSpringer, Dordrecht, 2006."},{"key":"2023033110105325051_j_cmam-2018-0019_ref_003_w2aab3b7e2132b1b6b1ab2ab3Aa","unstructured":"N.  Buong,\nConvergence rates in regularization for nonlinear ill-posed equations under accretive perturbations,\nZh. Vychisl. Mat. Mat. Fiz. 44 (2004), no. 3, 397\u2013402."},{"key":"2023033110105325051_j_cmam-2018-0019_ref_004_w2aab3b7e2132b1b6b1ab2ab4Aa","unstructured":"N.  Buong,\nOn nonlinear ill-posed accretive equations,\nSoutheast Asian Bull. Math. 28 (2004), no. 4, 595\u2013600."},{"key":"2023033110105325051_j_cmam-2018-0019_ref_005_w2aab3b7e2132b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"N.  Buong and N. T. H.  Phuong,\nConvergence rates in regularization for nonlinear ill-posed equations involving m-accretive mappings in Banach spaces,\nAppl. Math. Sci. (Ruse) 6 (2012), no. 61\u201364, 3109\u20133117.","DOI":"10.3103\/S1066369X13020072"},{"key":"2023033110105325051_j_cmam-2018-0019_ref_006_w2aab3b7e2132b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"H.  Egger and A.  Neubauer,\nPreconditioning Landweber iteration in Hilbert scales,\nNumer. Math. 101 (2005), no. 4, 643\u2013662.","DOI":"10.1007\/s00211-005-0622-5"},{"key":"2023033110105325051_j_cmam-2018-0019_ref_007_w2aab3b7e2132b1b6b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"H. W.  Engl, M.  Hanke and A.  Neubauer,\nRegularization of Inverse Problems,\nMath. 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