{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:25:14Z","timestamp":1760243114975,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2015,9,22]],"date-time":"2015-09-22T00:00:00Z","timestamp":1442880000000},"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, a general family of n-point Newton type iterative methods for solving nonlinear equations is constructed by using direct Hermite interpolation. The order of convergence of the new n-point iterative methods without memory is 2n requiring the evaluations of n functions and one first-order derivative in per full iteration, which implies that this family is optimal according to Kung and Traub\u2019s conjecture (1974). Its error equations and asymptotic convergence constants are obtained. The n-point iterative methods with memory are obtained by using a self-accelerating parameter, which achieve much faster convergence than the corresponding n-point methods without memory. The increase of convergence order is attained without any additional calculations so that the n-point Newton type iterative methods with memory possess a very high computational efficiency. Numerical examples are demonstrated to confirm theoretical results.<\/jats:p>","DOI":"10.3390\/a8030786","type":"journal-article","created":{"date-parts":[[2015,9,22]],"date-time":"2015-09-22T15:36:54Z","timestamp":1442936214000},"page":"786-798","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A Family of Newton Type Iterative Methods for Solving Nonlinear Equations"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8524-6488","authenticated-orcid":false,"given":"Xiaofeng","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, Bohai University, Jinzhou 121013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuping","family":"Qin","sequence":"additional","affiliation":[{"name":"College of Engineering, Bohai University, Jinzhou 121013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiyi","family":"Qian","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Bohai University, Jinzhou 121013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sheng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Bohai University, Jinzhou 121013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaodong","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Bohai University, Jinzhou 121013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,9,22]]},"reference":[{"key":"ref_1","unstructured":"Ortega, J.M., and Rheinbolt, W.C. 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