{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T12:34:59Z","timestamp":1648816499721},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2008,1,22]],"date-time":"2008-01-22T00:00:00Z","timestamp":1200960000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2008,2]]},"DOI":"10.1007\/s11075-007-9154-7","type":"journal-article","created":{"date-parts":[[2008,1,21]],"date-time":"2008-01-21T15:13:04Z","timestamp":1200928384000},"page":"157-167","source":"Crossref","is-referenced-by-count":0,"title":["On the convergence of the midpoint method"],"prefix":"10.1007","volume":"47","author":[{"given":"Ioannis K.","family":"Argyros","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Livinus U.","family":"Uko","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,1,22]]},"reference":[{"key":"9154_CR1","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1137\/0723011","volume":"23","author":"F.L. Allgower","year":"1986","unstructured":"Allgower, F.L., B\u00f6hmer, K., Potra, F.A., Rheinboldt, W.C.: A mesh independence principle for operator equations and their discretizations. SIAM J. Numer. Anal. 23, 160\u2013169 (1986)","journal-title":"SIAM J. Numer. Anal."},{"key":"9154_CR2","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.camwa.2005.01.002","volume":"49","author":"S. Amat","year":"2005","unstructured":"Amat, S., Busquier, S.: Convergence and numerical analysis of a family of two-step Steffensen\u2019s method. Comput. Math. Appl. 49, 13\u201322 (2005)","journal-title":"Comput. Math. Appl."},{"issue":"4","key":"9154_CR3","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/0893-9659(92)90076-L","volume":"5","author":"I.K. Argyros","year":"1992","unstructured":"Argyros, I.K., Chen, D.: The midpoint method for solving equations in Banach spaces. Appl. Math. Lett. 5(4), 7\u20139 (1992)","journal-title":"Appl. Math. Lett."},{"key":"9154_CR4","unstructured":"Argyros, I.K., Chen, D.: On the midpoint iterative method for solving nonlinear operator equations and applications to the solution of integral equations. Revue d\u2019analyse Num\u00e9rique et de th\u00e9orie de l\u2019approximation, Tome 23, fasc. 2, 139\u2013152 (1994)"},{"key":"9154_CR5","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1016\/j.jmaa.2004.04.008","volume":"298","author":"I.K. Argyros","year":"2004","unstructured":"Argyros, I.K.: A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space. J. Math. Anal. Appl. 298, 374\u2013387 (2004)","journal-title":"J. Math. Anal. Appl."},{"key":"9154_CR6","volume-title":"Series: Studies in Computational Mathematics 15","author":"I.K. Argyros","year":"2007","unstructured":"Argyros, I.K.: Computational Theory of Iterative Methods. In: Chui, C.K., Wuytack, L. (eds.) Series: Studies in Computational Mathematics 15. Elsevier Publ. Co., New York, USA (2007)"},{"key":"9154_CR7","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1137\/0724031","volume":"24","author":"P.N. Brown","year":"1987","unstructured":"Brown, P.N.: A local convergence theory for combined inexact-Newton\/finite-difference projection methods. SIAM J. Numer. Anal. 24, 407\u2013434 (1987)","journal-title":"SIAM J. Numer. Anal."},{"key":"9154_CR8","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1080\/00207169508804427","volume":"57","author":"J.A. Gutierrez","year":"1995","unstructured":"Gutierrez, J.A., Hernandez, M.A., Salanova, M.A.: Accessibility of solutions by Newton\u2019s method. Int. J. Comput. Math. 57, 239\u2013247 (1995)","journal-title":"Int. J. Comput. Math."},{"key":"9154_CR9","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.cam.2003.12.041","volume":"169","author":"H.H.H. Homeier","year":"2004","unstructured":"Homeier, H.H.H.: A modified Newton method with cubic convergence: the multivariable case. J. Comput. Appl. Math. 169, 161\u2013169 (2004)","journal-title":"J. Comput. Appl. Math."},{"key":"9154_CR10","volume-title":"Functional Analysis in Normed Spaces","author":"L.V. Kantorovich","year":"1982","unstructured":"Kantorovich, L.V., Akilov, G.P.: Functional Analysis in Normed Spaces. Pergamon Press, Oxford (1982)"},{"key":"9154_CR11","volume-title":"Iterative Solution of Nonlinear Equations in Several Variables","author":"J.M. Ortega","year":"1970","unstructured":"Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970)"},{"key":"9154_CR12","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1016\/S0893-9659(04)90104-8","volume":"17","author":"A.Y. \u00d6zban","year":"2004","unstructured":"\u00d6zban, A.Y.: Some new variants of Newton\u2019s method. Appl. Math. Lett. 17, 677\u2013682 (2004)","journal-title":"Appl. Math. Lett."},{"key":"9154_CR13","doi-asserted-by":"crossref","first-page":"129","DOI":"10.4064\/-3-1-129-142","volume":"3","author":"W.C. Rheinboldt","year":"1977","unstructured":"Rheinboldt, W.C.: An adaptive continuation process for solving systems of nonlinear equations. Banach Cent. Publ. 3, 129\u2013142 (1977)","journal-title":"Banach Cent. Publ."},{"key":"9154_CR14","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/BF01397005","volume":"32","author":"W. Werner","year":"1979","unstructured":"Werner, W.: \u00dcber ein Verfahren der Ordung $1 + \\sqrt 2 $ zur Nullstellenbestimmung. Numer. Math. 32, 333\u2013342 (1979)","journal-title":"Numer. Math."},{"key":"9154_CR15","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1137\/0721040","volume":"21","author":"T.J. Ypma","year":"1984","unstructured":"Ypma, T.J.: Local convergence of inexact Newton methods. SIAM J. Numer. Anal. 21, 583\u2013590 (1984)","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-007-9154-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-007-9154-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-007-9154-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T05:08:10Z","timestamp":1559365690000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-007-9154-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1,22]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2008,2]]}},"alternative-id":["9154"],"URL":"https:\/\/doi.org\/10.1007\/s11075-007-9154-7","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1,22]]}}}