{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T18:24:48Z","timestamp":1761157488410,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T00:00:00Z","timestamp":1675987200000},"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 provide a detailed local convergence analysis of a one-parameter family of iteration methods for the simultaneous approximation of polynomial zeros due to Ivanov (Numer. Algor. 75(4): 1193\u20131204, 2017). Thus, we obtain two local convergence theorems that provide sufficient conditions to guarantee the Q-cubic convergence of all members of the family. Among the other contributions, our results unify the latest such kind of results of the well known Dochev\u2013Byrnev and Ehrlich methods. Several practical applications are further given to emphasize the advantages of the studied family of methods and to show the applicability of the theoretical results.<\/jats:p>","DOI":"10.3390\/a16020103","type":"journal-article","created":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T01:48:56Z","timestamp":1676252936000},"page":"103","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Local Convergence Analysis of a One Parameter Family of Simultaneous Methods with Applications to Real-World Problems"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3219-9929","authenticated-orcid":false,"given":"Tsonyo M.","family":"Pavkov","sequence":"first","affiliation":[{"name":"Faculty of Physics and Technology, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valentin G.","family":"Kabadzhov","sequence":"additional","affiliation":[{"name":"Faculty of Physics and Technology, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ivan K.","family":"Ivanov","sequence":"additional","affiliation":[{"name":"Faculty of Physics and Technology, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0082-7791","authenticated-orcid":false,"given":"Stoil I.","family":"Ivanov","sequence":"additional","affiliation":[{"name":"Faculty of Physics and Technology, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,10]]},"reference":[{"key":"ref_1","first-page":"1085","article-title":"Neuer Beweis des Satzes, dass jede ganze rationale Function einer Ver\u00e4nderlichen dargestellt werden kann als ein Product aus linearen Functionen derselben Ver\u00e4nderlichen","volume":"II","author":"Weierstrass","year":"1891","journal-title":"Sitzungsber. 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