{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:10:20Z","timestamp":1760235020410,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,7,21]],"date-time":"2021-07-21T00:00:00Z","timestamp":1626825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We develop a local convergence of an iterative method for solving nonlinear least squares problems with operator decomposition under the classical and generalized Lipschitz conditions. We consider the case of both zero and nonzero residuals and determine their convergence orders. We use two types of Lipschitz conditions (center and restricted region conditions) to study the convergence of the method. Moreover, we obtain a larger radius of convergence and tighter error estimates than in previous works. Hence, we extend the applicability of this method under the same computational effort.<\/jats:p>","DOI":"10.3390\/axioms10030158","type":"journal-article","created":{"date-parts":[[2021,7,21]],"date-time":"2021-07-21T11:53:23Z","timestamp":1626868403000},"page":"158","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Gauss\u2013Newton\u2013Secant Method for Solving Nonlinear Least Squares Problems under Generalized Lipschitz Conditions"],"prefix":"10.3390","volume":"10","author":[{"given":"Ioannis K.","family":"Argyros","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3845-6260","authenticated-orcid":false,"given":"Stepan","family":"Shakhno","sequence":"additional","affiliation":[{"name":"Department of Theory of Optimal Processes, Ivan Franko National University of Lviv, Universytetska Str. 1, 79000 Lviv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roman","family":"Iakymchuk","sequence":"additional","affiliation":[{"name":"PEQUAN, LIP6, Sorbonne Universit\u00e9, 4 Place Jussieu, 75252 Paris, France"},{"name":"Fraunhofer ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Halyna","family":"Yarmola","sequence":"additional","affiliation":[{"name":"Department of Computational Mathematics, Ivan Franko National University of Lviv, Universytetska Str. 1, 79000 Lviv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael I.","family":"Argyros","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Oklahoma, Norman, OK 73071, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1016\/S0898-1221(04)90086-7","article-title":"Convergence and uniqueness properties of Gauss-Newton\u2019s method","volume":"47","author":"Li","year":"2004","journal-title":"Comput. 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