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In this paper, we justify why this expression is obtained. This is done by studying the symmetries of the operators obtained after applying Newton-like algorithms to a family of degree <jats:italic>d<\/jats:italic> polynomials <jats:italic>p<\/jats:italic>(<jats:italic>z<\/jats:italic>) = <jats:italic>z<\/jats:italic><jats:sup><jats:italic>d<\/jats:italic><\/jats:sup> \u2212 <jats:italic>c<\/jats:italic>. Moreover, we provide an iterative procedure to obtain the expression of new Newton-like algorithms. We also carry out a dynamical study of the given generic operator and provide general conclusions of this type of methods.<\/jats:p>","DOI":"10.1007\/s11075-022-01474-w","type":"journal-article","created":{"date-parts":[[2022,12,15]],"date-time":"2022-12-15T11:04:03Z","timestamp":1671102243000},"page":"1453-1480","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Dynamics of Newton-like root finding methods"],"prefix":"10.1007","volume":"93","author":[{"given":"B.","family":"Campos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.","family":"Canela","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P.","family":"Vindel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,12,15]]},"reference":[{"issue":"3","key":"1474_CR1","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1007\/s00010-004-2733-y","volume":"69","author":"S Amat","year":"2005","unstructured":"Amat, S., Busquier, S., Plaza, S.: Dynamics of the King and Jarratt iterations. 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