{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:10:24Z","timestamp":1760242224888,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,1,9]],"date-time":"2017-01-09T00:00:00Z","timestamp":1483920000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, we propose an algorithm to estimate the radius of convergence for the Picard iteration in the setting of a real Hilbert space. Numerical experiments show that the proposed algorithm provides convergence balls close to or even identical to the best ones. As the algorithm does not require to evaluate the norm of derivatives, the computing effort is relatively low.<\/jats:p>","DOI":"10.3390\/a10010010","type":"journal-article","created":{"date-parts":[[2017,1,9]],"date-time":"2017-01-09T11:03:23Z","timestamp":1483959803000},"page":"10","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Estimating the Local Radius of Convergence for Picard Iteration"],"prefix":"10.3390","volume":"10","author":[{"given":"\u015etefan","family":"M\u0103ru\u015fter","sequence":"first","affiliation":[{"name":"Department of Informatics, West University of Timisoara, B-dul V. Parvan No. 4, 300223 Timisoara, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2017,1,9]]},"reference":[{"key":"ref_1","unstructured":"Ostrowski, A.M. (1966). Solution of Equations and System of Equations, Academic Press. 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Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.na.2005.02.113","article-title":"Concerning the \u201cterra ingognita\u201d between convergence regions of two Newton methods","volume":"62","author":"Argyros","year":"2005","journal-title":"Nonlinear Anal."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1016\/j.jmaa.2004.04.008","article-title":"A unifyng local-semilocal convergence analysis and applications for two-points Newton methods in Banach spaces","volume":"298","author":"Argyros","year":"2004","journal-title":"J. Math. Anal. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1093\/imanum\/drn036","article-title":"Local convergence of Newton method in Banach spaces from the viewpoint of the majorant principle","volume":"29","author":"Frerreira","year":"2009","journal-title":"IMA J. Numer. 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Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"747","DOI":"10.2140\/pjm.1969.30.747","article-title":"Mean value iteration for nonexpansive mappings in a Banach space","volume":"30","author":"Outlaw","year":"1969","journal-title":"Pac. J. Math."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1090\/S0002-9939-1974-0346608-8","article-title":"Approximating fixed points of nonexpansive mappings","volume":"44","author":"Senter","year":"1974","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1090\/S0002-9939-1977-0636944-2","article-title":"The solution by iteration of nonlinear equations in Hilbert spaces","volume":"63","author":"Maruster","year":"1977","journal-title":"Proc. Am. Math. 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