{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:50:00Z","timestamp":1760241000679,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2019,11,6]],"date-time":"2019-11-06T00:00:00Z","timestamp":1572998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PGC2018-095896-B-C22"],"award-info":[{"award-number":["PGC2018-095896-B-C22"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003359","name":"Generalitat Valenciana","doi-asserted-by":"publisher","award":["PROMETEO\/2016\/089"],"award-info":[{"award-number":["PROMETEO\/2016\/089"]}],"id":[{"id":"10.13039\/501100003359","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>It is well known that scalar iterative methods with derivatives are highly more stable than their derivative-free partners, understanding the term stability as a measure of the wideness of the set of converging initial estimations. In multivariate case, multidimensional dynamical analysis allows us to afford this task and it is made on different Jacobian-free variants of Newton\u2019s method, whose estimations of the Jacobian matrix have increasing order. The respective basins of attraction and the number of fixed and critical points give us valuable information in this sense.<\/jats:p>","DOI":"10.3390\/a12110236","type":"journal-article","created":{"date-parts":[[2019,11,7]],"date-time":"2019-11-07T06:52:36Z","timestamp":1573109556000},"page":"236","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Stability Analysis of Jacobian-Free Newton\u2019s Iterative Method"],"prefix":"10.3390","volume":"12","author":[{"given":"Abdolreza","family":"Amiri","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Razi University, 67149 Kermanshah, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7462-9173","authenticated-orcid":false,"given":"Alicia","family":"Cordero","sequence":"additional","affiliation":[{"name":"Institute for Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5065-1571","authenticated-orcid":false,"given":"Mohammad Taghi","family":"Darvishi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Razi University, 67149 Kermanshah, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9893-0761","authenticated-orcid":false,"given":"Juan R.","family":"Torregrosa","sequence":"additional","affiliation":[{"name":"Institute for Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,6]]},"reference":[{"key":"ref_1","unstructured":"Ortega, J.M., and Rheinboldt, W.C. 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Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1344","DOI":"10.1007\/s10910-018-0971-9","article-title":"Stability analysis of Jacobian-free iterative methods for solving nonlinear systems by using families of mth power divided differences","volume":"57","author":"Amiri","year":"2019","journal-title":"J. Math. Chem."},{"key":"ref_6","first-page":"3","article-title":"Review of some iterative root\u2013finding methods from a dynamical point of view","volume":"10","author":"Amat","year":"2004","journal-title":"Scientia"},{"key":"ref_7","first-page":"567","article-title":"Basins of attraction for optimal eighth order methods to find simple roots of nonlinear equations","volume":"227","author":"Neta","year":"2014","journal-title":"Appl. Math. 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(2013). Drawing dynamical and parameter planes of iterative families and methods. Sci. World J., 2013.","DOI":"10.1155\/2013\/780153"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/11\/236\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:32:26Z","timestamp":1760189546000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/11\/236"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,6]]},"references-count":16,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["a12110236"],"URL":"https:\/\/doi.org\/10.3390\/a12110236","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2019,11,6]]}}}