{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T19:39:49Z","timestamp":1775936389322,"version":"3.50.1"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,12,24]],"date-time":"2021-12-24T00:00:00Z","timestamp":1640304000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,12,24]],"date-time":"2021-12-24T00:00:00Z","timestamp":1640304000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12771210"],"award-info":[{"award-number":["12771210"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100012554","name":"Hubei provincial department of education","doi-asserted-by":"publisher","award":["B2020151"],"award-info":[{"award-number":["B2020151"]}],"id":[{"id":"10.13039\/100012554","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100012554","name":"Hubei provincial department of education","doi-asserted-by":"publisher","award":["2020628"],"award-info":[{"award-number":["2020628"]}],"id":[{"id":"10.13039\/100012554","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009558","name":"University Natural Science Research Project of Anhui Province","doi-asserted-by":"publisher","award":["KJ2020ZD008"],"award-info":[{"award-number":["KJ2020ZD008"]}],"id":[{"id":"10.13039\/501100009558","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2022,12]]},"DOI":"10.1007\/s12190-021-01599-6","type":"journal-article","created":{"date-parts":[[2021,12,24]],"date-time":"2021-12-24T14:02:17Z","timestamp":1640354537000},"page":"3655-3671","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Improved convergence results of an efficient Levenberg\u2013Marquardt method for nonlinear equations"],"prefix":"10.1007","volume":"68","author":[{"given":"Meilan","family":"Zeng","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8395-6400","authenticated-orcid":false,"given":"Guanghui","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,12,24]]},"reference":[{"key":"1599_CR1","unstructured":"Ahookhosh, M.A., Francisco, J.A., Fleming, R.M.T., et\u00a0al.: Local convergence of the Levenberg\u2013Marquardt method under H$$\\ddot{o}$$lder metric subregularity. arXiv: 1703.07461"},{"issue":"5","key":"1599_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/02331934.2018.1435655","volume":"67","author":"K Amini","year":"2018","unstructured":"Amini, K., Rostami, F., Caristi, G.: An efficient Levenberg\u2013Marquardt method with a new LM parameter for systems of nonlinear equations. Optimization 67(5), 1\u201314 (2018)","journal-title":"Optimization"},{"issue":"1\u20132","key":"1599_CR3","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/s10107-011-0486-7","volume":"137","author":"R Behling","year":"2013","unstructured":"Behling, R., Iusem, A.: The effect of calmness on the solution set of systems of nonlinear equations. Math. Program. 137(1\u20132), 155\u2013165 (2013)","journal-title":"Math. Program."},{"key":"1599_CR4","volume-title":"Numerical Methods for Unconstrained Optimization and Nonlinear Equation","author":"JE Dennis","year":"2009","unstructured":"Dennis, J.E., Schnabel, R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equation. Science Press, Beijing (2009)"},{"issue":"1","key":"1599_CR5","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/s00607-004-0083-1","volume":"74","author":"JY Fan","year":"2005","unstructured":"Fan, J.Y., Yuan, Y.X.: On the quadratic convergence of the Levenberg\u2013Marquardt method without nonsingularity assumption. Computing 74(1), 23\u201339 (2005)","journal-title":"Computing"},{"issue":"5","key":"1599_CR6","first-page":"625","volume":"21","author":"JY Fan","year":"2003","unstructured":"Fan, J.Y.: A modified Levenberg\u2013Marquardt algorithm for singular system of nonlinear equations. J. Comput. Math. 21(5), 625\u2013636 (2003)","journal-title":"J. Comput. Math."},{"issue":"1","key":"1599_CR7","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1007\/s10915-018-0777-8","volume":"78","author":"JY Fan","year":"2019","unstructured":"Fan, J.Y., Huang, J.C., Pan, J.Y.: An adaptive multi-step Levenberg\u2013Marquardt method. J. Sci. Comput. 78(1), 531\u2013548 (2019)","journal-title":"J. Sci. Comput."},{"issue":"14","key":"1599_CR8","doi-asserted-by":"publisher","first-page":"3186","DOI":"10.1080\/00207160802691645","volume":"87","author":"JY Fan","year":"2010","unstructured":"Fan, J.Y., Pan, J.Y.: A modified trust region algorithm for nonlinear equations with new updating rule of trust region radius. Int. J. Comput. Math. 87(14), 3186\u20133195 (2010)","journal-title":"Int. J. Comput. Math."},{"key":"1599_CR9","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1090\/qam\/10666","volume":"2","author":"K Levenberg","year":"1944","unstructured":"Levenberg, K.: A method for the solution of certain nonlinear problems in least squares. Quart. Appl. Math. 2, 164\u2013168 (1944)","journal-title":"Quart. Appl. Math."},{"issue":"1","key":"1599_CR10","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1137\/S0036142998335704","volume":"37","author":"DH Li","year":"1999","unstructured":"Li, D.H., Fukushima, M.: A global and superlinear convergent Gauss-Newton-based BFGS method for symmetric nonlinear equations. SIAM J. Numer. Anal. 37(1), 152\u2013172 (1999)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"1599_CR11","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1080\/10556780008805782","volume":"13","author":"DH Li","year":"2000","unstructured":"Li, D.H., Fukushima, M.: A derivative-free line search and global convergence of Broyden-like method for nonlinear equations. Optim. Methods Softw. 13(3), 181\u2013201 (2000)","journal-title":"Optim. Methods Softw."},{"key":"1599_CR12","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1137\/0111030","volume":"11","author":"DW Marquardt","year":"1963","unstructured":"Marquardt, D.W.: An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math. 11, 431\u2013441 (1963)","journal-title":"J. Soc. Ind. Appl. Math."},{"issue":"1","key":"1599_CR13","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1145\/355934.355936","volume":"7","author":"JJ Mor\u00e9","year":"1981","unstructured":"Mor\u00e9, J.J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained optimization software. ACM Trans. Math. Softw. 7(1), 17\u201341 (1981)","journal-title":"ACM Trans. Math. Softw."},{"issue":"5","key":"1599_CR14","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1137\/0721054","volume":"21","author":"RB Schnabel","year":"1984","unstructured":"Schnabel, R.B., Frank, P.D.: Tensor methods for nonlinear equations. SIAM J. Numer. Anal. 21(5), 815\u2013843 (1984)","journal-title":"SIAM J. Numer. Anal."},{"key":"1599_CR15","volume-title":"Matrix Perturbation Theory","author":"GW Stewart","year":"1990","unstructured":"Stewart, G.W., Sun, J.G.: Matrix Perturbation Theory. Academic Press Boston, San Diego (1990)"},{"key":"1599_CR16","first-page":"1","volume":"17","author":"HY Wang","year":"2019","unstructured":"Wang, H.Y., Fan, J.Y.: Convergence rate of the Levenberg\u2013Marquardt method under H$$\\ddot{o}$$lderian local error bound. Optim. Methods Softw. 17, 1\u201320 (2019)","journal-title":"Optim. Methods Softw."},{"key":"1599_CR17","doi-asserted-by":"publisher","first-page":"2265","DOI":"10.3934\/jimo.2020068","volume":"17","author":"HY Wang","year":"2021","unstructured":"Wang, H.Y., Fan, J.Y.: Convergence properties of inexact Levenberg\u2013Marquardt method under H$$\\ddot{o}$$lderian local error bound. J. Ind. Manag. Optim. 17, 2265\u20132275 (2021)","journal-title":"J. Ind. Manag. Optim."},{"key":"1599_CR18","first-page":"239","volume":"15","author":"N Yamashita","year":"2001","unstructured":"Yamashita, N., Fukushima, M.: On the rate of convergence of the Levenberg\u2013Marquardt method. Computing 15, 239\u2013249 (2001)","journal-title":"Computing"},{"key":"1599_CR19","first-page":"7","volume":"1","author":"YX Yuan","year":"1998","unstructured":"Yuan, Y.X.: Trust region algorithm for nonlinear equations. Information 1, 7\u201321 (1998)","journal-title":"Information"},{"issue":"2","key":"1599_CR20","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/s001860300302","volume":"58","author":"JL Zhang","year":"2003","unstructured":"Zhang, J.L., Wang, Y.: A new trust region method for nonlinear equations. Math. Methods Oper. Res. 58(2), 283\u2013298 (2003)","journal-title":"Math. Methods Oper. Res."},{"issue":"4","key":"1599_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/10556788.2016.1171863","volume":"31","author":"X Zhu","year":"2016","unstructured":"Zhu, X., Lin, G.H.: Improved convergence results for a modified Levenberg\u2013Marquardt method for nonlinear equations and applications in MPCC. Optim. Methods Softw. 31(4), 1\u201314 (2016)","journal-title":"Optim. Methods Softw."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-021-01599-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-021-01599-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-021-01599-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,5]],"date-time":"2022-12-05T16:12:16Z","timestamp":1670256736000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-021-01599-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,24]]},"references-count":21,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["1599"],"URL":"https:\/\/doi.org\/10.1007\/s12190-021-01599-6","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,24]]},"assertion":[{"value":"1 April 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 July 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 July 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 December 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}