{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:46:46Z","timestamp":1753886806539,"version":"3.41.2"},"reference-count":17,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,9,29]],"date-time":"2012-09-29T00:00:00Z","timestamp":1348876800000},"content-version":"vor","delay-in-days":272,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100006280","name":"Ministerio de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["MTM2011-28636-C02-02"],"award-info":[{"award-number":["MTM2011-28636-C02-02"]}],"id":[{"id":"10.13039\/501100006280","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fondo Nacional de Innovaci\u00f3n y Desarrollo Cient\u00edfica","award":["MTM2011-28636-C02-02"],"award-info":[{"award-number":["MTM2011-28636-C02-02"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>A new set of predictor\u2010corrector iterative methods with increasing order of convergence is proposed in order to estimate the solution of nonlinear systems. Our aim is to achieve high order of convergence with few Jacobian and\/or functional evaluations. Moreover, we pay special attention to the number of linear systems to be solved in the process, with different matrices of coefficients. On the other hand, by applying the pseudocomposition technique on each proposed scheme we get to increase their order of convergence, obtaining new efficient high\u2010order methods. We use the classical efficiency index to compare the obtained procedures and make some numerical test, that allow us to confirm the theoretical results.<\/jats:p>","DOI":"10.1155\/2012\/709843","type":"journal-article","created":{"date-parts":[[2012,10,1]],"date-time":"2012-10-01T04:07:47Z","timestamp":1349064467000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["New Predictor\u2010Corrector Methods with High Efficiency for Solving Nonlinear Systems"],"prefix":"10.1155","volume":"2012","author":[{"given":"Alicia","family":"Cordero","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan R.","family":"Torregrosa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mar\u00eda P.","family":"Vassileva","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2012,9,29]]},"reference":[{"volume-title":"Nontrivial Methods in Numerical Analysis: Selected Topics in Numerical Analysis","year":"2010","author":"Iliev A.","key":"e_1_2_5_1_2"},{"key":"e_1_2_5_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0009-2509(77)80203-0"},{"key":"e_1_2_5_3_2","first-page":"23","article-title":"Chebyshev-like methods and quadratic equations","volume":"28","author":"Ezquerro J. 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