{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:44:39Z","timestamp":1776843879339,"version":"3.51.2"},"reference-count":12,"publisher":"American Mathematical Society (AMS)","issue":"273","license":[{"start":{"date-parts":[[2011,7,8]],"date-time":"2011-07-08T00:00:00Z","timestamp":1310083200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    A semilocal convergence analysis for directional Newton methods in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n\">\n                        <mml:semantics>\n                          <mml:mi>n<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -variables is provided in this study. Using weaker hypotheses than in the elegant related work by Y. Levin and A. Ben-Israel and introducing the center-Lipschitz condition we provide under the same computational cost as in Levin and Ben-Israel a semilocal convergence analysis with the following advantages: weaker convergence conditions; larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location of the zero of the function. A numerical example where our results apply to solve an equation but not the ones in Levin and Ben-Israel is also provided in this study.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2010-02398-1","type":"journal-article","created":{"date-parts":[[2010,10,4]],"date-time":"2010-10-04T11:01:54Z","timestamp":1286190114000},"page":"327-343","source":"Crossref","is-referenced-by-count":83,"title":["A semilocal convergence analysis for directional Newton methods"],"prefix":"10.1090","volume":"80","author":[{"given":"Ioannis","family":"Argyros","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2010,7,8]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/j.cam.2004.01.029","article-title":"On the Newton-Kantorovich hypothesis for solving equations","volume":"169","author":"Argyros, Ioannis K.","year":"2004","journal-title":"J. Comput. Appl. 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