{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T15:04:14Z","timestamp":1785337454353,"version":"3.55.0"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2014,5,3]],"date-time":"2014-05-03T00:00:00Z","timestamp":1399075200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2015,2]]},"DOI":"10.1007\/s11075-014-9843-y","type":"journal-article","created":{"date-parts":[[2014,5,2]],"date-time":"2014-05-02T03:42:54Z","timestamp":1399002174000},"page":"261-288","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":52,"title":["A new class of three-point methods with optimal convergence order eight and its dynamics"],"prefix":"10.1007","volume":"68","author":[{"given":"Taher","family":"Lotfi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Somayeh","family":"Sharifi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mehdi","family":"Salimi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefan","family":"Siegmund","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2014,5,3]]},"reference":[{"key":"9843_CR1","unstructured":"Amat, S., Busquier, S., Plaza, S.: Iterative root-finding methods. Unpublished report (2004)"},{"key":"9843_CR2","first-page":"3","volume":"10","author":"S Amat","year":"2004","unstructured":"Amat, S., Busquier, S., Plaza, S.: Review of some iterative root-finding methods from a dynamical point of view. J. Sci. 10, 3\u201335 (2004)","journal-title":"J. Sci."},{"key":"9843_CR3","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1016\/S0096-3003(03)00747-1","volume":"154","author":"S Amat","year":"2004","unstructured":"Amat, S., Busquirer, S., Plaza, S.: Dynamics of a family of third-order itrative methods that do not require using second derivatives. J. Appl. Math. Comput. 154, 735\u2013746 (2004)","journal-title":"J. Appl. Math. Comput."},{"key":"9843_CR4","doi-asserted-by":"crossref","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. J. Aeq. Math. 69, 212\u2013223 (2005)","journal-title":"J. Aeq. Math."},{"issue":"(1)","key":"9843_CR5","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s11075-013-9699-6","volume":"65","author":"DKR Babajee","year":"2014","unstructured":"Babajee, D.K.R., Cordero, A., Soleymani, F., Torregrosa, J.R.: On improved three-step schemes with high efficiency index and their dynamics. J. Numer. Algorithms 65(1), 153-169 (2013)","journal-title":"J. Numer. Algorithms"},{"key":"9843_CR6","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.cam.2008.07.004","volume":"225","author":"W Bi","year":"2009","unstructured":"Bi, W., Ren, H., Wu, Q.: Three-step iterative methods with eighth-order convergence for solving nonlinear equations. J. Comput. Appl. Math. 225, 105\u2013112 (2009)","journal-title":"J. Comput. Appl. Math."},{"key":"9843_CR7","doi-asserted-by":"crossref","first-page":"6427","DOI":"10.1016\/j.amc.2011.12.013","volume":"218","author":"C Chun","year":"2012","unstructured":"Chun, C., Lee, M.Y., Neta, B., Dzunic, J.: On optimal fourth-order iterative methods free from second derivative and their dynamics. J. Appl. Math. Comput. 218, 6427\u20136438 (2012)","journal-title":"J. Appl. Math. Comput."},{"key":"9843_CR8","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1016\/j.amc.2013.08.033","volume":"223","author":"C Chun","year":"2013","unstructured":"Chun, C., Lee, M.Y.: A new optimal eighth-order family of iterative methods for the solution of nonlinear equations. J. Appl. Math. Comput. 223, 506\u2013519 (2013)","journal-title":"J. Appl. Math. Comput."},{"key":"9843_CR9","doi-asserted-by":"crossref","unstructured":"Cordero, A., Fardi, M., Ghasemi, M., Torregrosa, J.R.: Accelerated iterative methods for finding solutions of nonlinear equations and their dynamical behavior. J. Calcolo, 1\u201314 (2012)","DOI":"10.1007\/s10092-012-0073-1"},{"key":"9843_CR10","doi-asserted-by":"crossref","first-page":"3189","DOI":"10.1016\/j.cam.2011.01.004","volume":"235","author":"A Cordero","year":"2011","unstructured":"Cordero, A., Torregrosa, J.R., Vassileva, M.P.: Three-step iterative methods with optimal eighth-order convergence. J. Comput. Appl. Math. 235, 3189\u20133194 (2011)","journal-title":"J. Comput. Appl. Math."},{"key":"9843_CR11","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-84996-251-3","volume-title":"Mathematica: A Problem-Centered Approach","author":"R Hazrat","year":"2010","unstructured":"Hazrat, R.: Mathematica: A Problem-Centered Approach. Springer-Verlag London Limited, Berlin (2010)"},{"key":"9843_CR12","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1090\/S0025-5718-66-99924-8","volume":"20","author":"P Jarratt","year":"1966","unstructured":"Jarratt, P.: Some fourth order multipoint iterative methods for solving equations. J. Math. Comput. 20, 434\u2013437 (1966)","journal-title":"J. Math. Comput."},{"key":"9843_CR13","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1137\/0710072","volume":"10","author":"RF King","year":"1973","unstructured":"King, R.F.: Family of four order methods for nonlinear equations. SIAM J. Numer. Anal. 10, 876\u2013879 (1973)","journal-title":"SIAM J. Numer. Anal."},{"key":"9843_CR14","first-page":"634","volume":"21","author":"HT Kung","year":"1974","unstructured":"Kung, H.T., Traub, J.F.: Optimal order of one-point and multipoint iteration. J. Assoc. Comput. Math. 21, 634\u2013651 (1974)","journal-title":"J. Assoc. Comput. Math."},{"key":"9843_CR15","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1080\/00207168108803257","volume":"9","author":"B Neta","year":"1981","unstructured":"Neta, B.: On a family of multipoint methods for nonlinear equations. Int. J. Comput. Math. 9, 353\u2013361 (1981)","journal-title":"Int. J. Comput. Math."},{"key":"9843_CR16","doi-asserted-by":"crossref","unstructured":"Neta, B., Chun, C., Scott, M.: Basin of attractions for optimal eighth order methods to find simpl roots of nonlinear equations. J. Appl. Math. Comput. Accepted (2013)","DOI":"10.1016\/j.amc.2013.02.035"},{"key":"9843_CR17","doi-asserted-by":"crossref","first-page":"5043","DOI":"10.1016\/j.amc.2011.10.071","volume":"218","author":"B Neta","year":"2012","unstructured":"Neta, B., Scott, M., Chun, C.: Basin attractors for various methods for multiple roots. J. Appl. Math. Comput. 218, 5043\u20135066 (2012)","journal-title":"J. Appl. Math. Comput."},{"key":"9843_CR18","doi-asserted-by":"crossref","first-page":"10548","DOI":"10.1016\/j.amc.2012.04.017","volume":"218","author":"B Neta","year":"2012","unstructured":"Neta, B., Scott, M., Chun, C.: Basin of attraction for several methods to find simple roots of nonlinear equations. J. Appl. Math. Comput. 218, 10548\u201310556 (2012)","journal-title":"J. Appl. Math. Comput."},{"key":"9843_CR19","volume-title":"Solution of Equations and Systems of Equations","author":"AM Ostrowski","year":"1966","unstructured":"Ostrowski, A.M.: Solution of Equations and Systems of Equations. Academic Press, New York (1966)"},{"key":"9843_CR20","volume-title":"Multipoint Methods for Solving Nonlinear Equations","author":"MS Petkovic","year":"2013","unstructured":"Petkovic, M.S., Neta, B., Petkovic, L.D., Dzunic, J.: Multipoint Methods for Solving Nonlinear Equations. Elsevier, Waltham (2013)"},{"key":"9843_CR21","doi-asserted-by":"crossref","first-page":"2584","DOI":"10.1016\/j.amc.2011.07.076","volume":"218","author":"M Scott","year":"2011","unstructured":"Scott, M., Neta, B., Chun, C.: Basin attractors for various methods. J. Appl. Math. Comput. 218, 2584\u20132599 (2011)","journal-title":"J. Appl. Math. Comput."},{"key":"9843_CR22","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/s11075-009-9345-5","volume":"54","author":"JR Sharma","year":"2010","unstructured":"Sharma, J.R., Sharma, R.: A new family of modified Ostrowski\u2019s methods with accelerated eighth order convergence. J. Numer. Algorithms 54, 445\u2013458 (2010)","journal-title":"J. Numer. Algorithms"},{"key":"9843_CR23","doi-asserted-by":"crossref","unstructured":"Soleymani, F., Lotfi, T., Bakhtiari, P.: A multi-step class of iterative methods for nonlinear systems, J. Optim. Lett. (2013)","DOI":"10.1007\/s11590-013-0617-6"},{"key":"9843_CR24","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/s10957-011-9929-9","volume":"153","author":"F Soleymani","year":"2012","unstructured":"Soleymani, F., Sharifi, M., Mousavi, B.S.: An improvement of Ostrowski\u2019s and King\u2019s techniques with optimal convergence order eight. J. Optim. Theory Appl. 153, 225\u2013236 (2012)","journal-title":"J. Optim. Theory Appl."},{"key":"9843_CR25","unstructured":"Stewart, B.D.: Attractor Basins of Various Root-Finding Methods M.S. thesis, Naval Postgraduate School, Department of Applied Mathematics, Monterey (2001)"},{"key":"9843_CR26","doi-asserted-by":"crossref","first-page":"2278","DOI":"10.1016\/j.cam.2009.10.012","volume":"233","author":"R Thukral","year":"2010","unstructured":"Thukral, R., Petkovic, M.S.: A family of three-point methods of optimal order for solving nonlinear equations. J. Comput. Appl. Math. 233, 2278\u20132284 (2010)","journal-title":"J. Comput. Appl. Math."},{"key":"9843_CR27","volume-title":"Iterative Methods for the Solution of Equations","author":"JF Traub","year":"1964","unstructured":"Traub, J.F.: Iterative Methods for the Solution of Equations. Prentice Hall, New York (1964)"},{"key":"9843_CR28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01401018","volume":"52","author":"ER Vrscay","year":"1988","unstructured":"Vrscay, E.R., Gilbert, W.J.: Extraneous fixed points, basin boundaries and chaotic dynamics for Schroder and Konig rational iteration functions. J. Numer. Math. 52, 1\u201316 (1988)","journal-title":"J. Numer. Math."},{"key":"9843_CR29","doi-asserted-by":"crossref","first-page":"1611","DOI":"10.1016\/j.cam.2010.03.002","volume":"234","author":"X Wang","year":"2010","unstructured":"Wang, X., Liu, L.: New eighth-order iterative methods for solving nonlinear equations. J. Comput. Appl. Math. 234, 1611\u20131620 (2010)","journal-title":"J. Comput. Appl. Math."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-014-9843-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-014-9843-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-014-9843-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,10]],"date-time":"2019-08-10T02:04:34Z","timestamp":1565402674000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-014-9843-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,3]]},"references-count":29,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,2]]}},"alternative-id":["9843"],"URL":"https:\/\/doi.org\/10.1007\/s11075-014-9843-y","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5,3]]}}}