{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T22:32:39Z","timestamp":1767825159103,"version":"3.49.0"},"reference-count":34,"publisher":"American Mathematical Society (AMS)","issue":"280","license":[{"start":{"date-parts":[[2013,4,2]],"date-time":"2013-04-02T00:00:00Z","timestamp":1364860800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>In this paper we investigate the regularizing properties of discretization in preimage space for linear and nonlinear ill-posed operator equations with noisy data. We propose to choose the discretization level, that acts as a regularization parameter in this context, by a discrepancy principle. While general convergence has been shown not to hold, we provide convergence results under appropriate conditions on the exact solution.<\/p>","DOI":"10.1090\/s0025-5718-2012-02596-8","type":"journal-article","created":{"date-parts":[[2012,4,2]],"date-time":"2012-04-02T14:57:58Z","timestamp":1333378678000},"page":"2049-2069","source":"Crossref","is-referenced-by-count":14,"title":["A convergence analysis of regularization by discretization in preimage space"],"prefix":"10.1090","volume":"81","author":[{"given":"Barbara","family":"Kaltenbacher","sequence":"first","affiliation":[]},{"given":"Jonas","family":"Offtermatt","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2012,4,2]]},"reference":[{"key":"1","series-title":"Mathematics and Its Applications (New York)","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4020-3122-9","volume-title":"Iterative methods for approximate solution of inverse problems","volume":"577","author":"Bakushinsky, A. 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