{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T14:58:58Z","timestamp":1772549938070,"version":"3.50.1"},"reference-count":21,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,4,25]],"date-time":"2017-04-25T00:00:00Z","timestamp":1493078400000},"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, we present a new sixth-order iterative method for solving nonlinear systems and prove a local convergence result. The new method requires solving five linear systems per iteration. An important feature of the new method is that the LU (lower upper, also called LU factorization) decomposition of the Jacobian matrix is computed only once in each iteration. The computational efficiency index of the new method is compared to that of some known methods. Numerical results are given to show that the convergence behavior of the new method is similar to the existing methods. The new method can be applied to small- and medium-sized nonlinear systems.<\/jats:p>","DOI":"10.3390\/a10020045","type":"journal-article","created":{"date-parts":[[2017,4,25]],"date-time":"2017-04-25T13:21:12Z","timestamp":1493126472000},"page":"45","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["An Efficient Sixth-Order Newton-Type Method for Solving Nonlinear Systems"],"prefix":"10.3390","volume":"10","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"}]},{"given":"Yang","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Information Engineering, Puyang Vocational and Technical College, Puyang 457000, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kelley, C.T. 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Lett."},{"key":"ref_5","first-page":"263","article-title":"On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods","volume":"237","author":"Noguera","year":"2013","journal-title":"J. Comput. Appl. Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4548","DOI":"10.1016\/j.amc.2010.11.006","article-title":"Efficient high-order methods based on golden ratio for nonlinear systems","volume":"217","author":"Cordero","year":"2011","journal-title":"Appl. Math. Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"11496","DOI":"10.1016\/j.amc.2012.04.081","article-title":"Pseudocomposition: A technique to design predictor-corrector methods for systems of nonlinear equations","volume":"218","author":"Cordero","year":"2012","journal-title":"Appl. Math. Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1007\/s11075-012-9685-4","article-title":"On the efficiency of two variants of Kurchatov\u2019s method for solving nonlinear systems","volume":"64","author":"Ezquerro","year":"2013","journal-title":"Numer. Algorithms"},{"key":"ref_9","unstructured":"Potra, F.A., and Pt\u00e1k, V. (1984). Nondiscrete Induction and Iterative Processes, Pitman Publishing."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2066","DOI":"10.1016\/j.camwa.2012.03.105","article-title":"Analysing the efficiency of some modifications of the secant method","volume":"64","author":"Ezquerro","year":"2012","journal-title":"Comput. Math. 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