{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T21:13:30Z","timestamp":1649020410204},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[1982,12,1]],"date-time":"1982-12-01T00:00:00Z","timestamp":407548800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[1982,12]]},"DOI":"10.1007\/bf02246758","type":"journal-article","created":{"date-parts":[[2005,11,14]],"date-time":"2005-11-14T20:10:48Z","timestamp":1131999048000},"page":"309-326","source":"Crossref","is-referenced-by-count":3,"title":["Variable Schrittweitensteuerungen f\u00fcr die Homotopiemethode bei ad\u00e4quaten nichtlinearen Ausgleichsproblemen"],"prefix":"10.1007","volume":"29","author":[{"given":"W. M.","family":"H\u00e4u\u00dfler","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"BF02246758_CR1","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/0022-247X(66)90115-6","volume":"15","author":"A. Ben-Israel","year":"1966","unstructured":"Ben-Israel, A.: A Newton-Raphson Method for the solution of equations. J. Math. Anal. Appl.15, 243\u2013252 (1966).","journal-title":"J. Math. Anal. Appl."},{"key":"BF02246758_CR2","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1090\/S0025-5718-1976-0395209-4","volume":"30","author":"P. T. Boggs","year":"1976","unstructured":"Boggs, P. T., Dennis, J. E., jr.: A stability analysis for perturbed nonlinear iterative methods. Math. Comp.30, 199\u2013215 (1976).","journal-title":"Math. Comp."},{"key":"BF02246758_CR3","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/BF01404679","volume":"18","author":"K. M. Brown","year":"1972","unstructured":"Brown, K. M., Dennis, J. E., jr.: Derivative free analogues of the Levenberg-Marquardt and Gauss Algorithms for nonlinear least squares approximations. Numer. Math.18, 289\u2013297 (1972).","journal-title":"Numer. Math."},{"key":"BF02246758_CR4","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1137\/0718066","volume":"18","author":"C. Heijer Den","year":"1981","unstructured":"Den Heijer, C., Rheinboldt, W. C.: On steplength algorithms for a class of continuation methods. SIAM J. Numer. Anal.18, 925\u2013948 (1981).","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02246758_CR5","unstructured":"Dennis, J. E., jr., Welsch, R. E.: Techniques for nonlinear least squares and robust regression. Proc. of the ASA Statistical Computing Section1976, 83\u201387."},{"key":"BF02246758_CR6","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/BF01399549","volume":"33","author":"P. Deuflhard","year":"1979","unstructured":"Deuflhard, P.: A stepsize control for continuation methods and its special application to multiple shooting techniques. Numer. Math.33, 115\u2013146 (1979).","journal-title":"Numer. Math."},{"key":"BF02246758_CR7","unstructured":"Deufhard, P., Apostolescu, V.: A study of the Gauss-Newton Algorithm for the solution of nonlinear least squares problems. In: Special topics of applied mathematics (Frehse, J., Pallaschke, D., Trottenberg, T., eds.) North-Holland 1980."},{"key":"BF02246758_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/0716001","volume":"16","author":"P. Deuflhard","year":"1979","unstructured":"Deuflhard P., Heindl, G.: Affine invariant convergence theorems for Newton's method and extensions to related methods. SIAM J. Numer. Anal.16, 1\u201310 (1979).","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02246758_CR9","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1007\/BF02241609","volume":"9","author":"M. Feilmeier","year":"1972","unstructured":"Feilmeier, M.: Numerische Aspekte beid er Einbettung nichtlinearer Probleme. Computing9, 355\u2013364 (1972).","journal-title":"Computing"},{"key":"BF02246758_CR10","unstructured":"Feilmeier, M., Lory, P., Scheuring, H., Wacker, Hj.: Einbettung. DFG \u2014 Berichte 1, 2, 3 (1973, 1974, 1975)."},{"key":"BF02246758_CR11","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1145\/321186.321200","volume":"10","author":"F. Freudenstein","year":"1963","unstructured":"Freudenstein, F., Roth, B.: Numerical solution of systems of nonlinear equations. J. Assoc. Comp. Math.10, 550\u2013556 (1963).","journal-title":"J. Assoc. Comp. Math."},{"key":"BF02246758_CR12","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1007\/BF01933641","volume":"20","author":"J. Hackl","year":"1980","unstructured":"Hackl, J., Wacker, Hj., Zulehner, W.: An efficient step size control for continuation methods. BIT20, 475\u2013485 (1980).","journal-title":"BIT"},{"key":"BF02246758_CR13","unstructured":"H\u00e4u\u00dfler, W. M.: Das Verfahren von Boggs und modifizierte Newtonverfahren. Diplomarbeit, Institut f\u00fcr Statistik und Unternehmungsforschung, TU M\u00fcnchen, 1975."},{"key":"BF02246758_CR14","first-page":"T421","volume":"58","author":"W. M. H\u00e4u\u00dfler","year":"1978","unstructured":"H\u00e4u\u00dfler, W. M.: Zu \u00fcber- und unterrelaxierten Newtonverfahren. ZAMM58, T421-T423 (1978).","journal-title":"ZAMM"},{"key":"BF02246758_CR15","first-page":"303","volume":"31","author":"W. M. H\u00e4u\u00dfler","year":"1979","unstructured":"H\u00e4u\u00dfler W. M., Bolkart, W.: Affin-invariante Konvergenzs\u00e4tze und automatische Schrittweitensteuerung f\u00fcr Einbettungsverfahren. Operations Research Verfahren31, 303\u2013312 (1979).","journal-title":"Operations Research Verfahren"},{"key":"BF02246758_CR16","unstructured":"Heindl, G.: Some remarks on the convergence of descent methods. In: Wacker (1979)."},{"key":"BF02246758_CR17","volume-title":"Methods for unconstrained optimization problems","author":"J. Kowalik","year":"1968","unstructured":"Kowalik, J., Osborne, M.: Methods for unconstrained optimization problems. New York: American Elsevier 1968."},{"key":"BF02246758_CR18","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1137\/0111030","volume":"11","author":"D. W. Marquardt","year":"1963","unstructured":"Marquardt, D. W.: An algorithm for least-squares-estimation of nonlinear parameters. SIAM J. Appl. Math.11, 431\u2013441 (1963).","journal-title":"SIAM J. Appl. Math."},{"key":"BF02246758_CR19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/1022001","volume":"22","author":"L. Nazareth","year":"1980","unstructured":"Nazareth, L.: Some recent approaches to solving large residual nonlinear least squares problems. SIAM Review22, 1\u201311 (1980).","journal-title":"SIAM Review"},{"key":"BF02246758_CR20","volume-title":"Iterative solution of nonlinear equations in several variables","author":"J. M. Ortega","year":"1970","unstructured":"Ortega, J. M., Reinboldt, W. C.: Iterative solution of nonlinear equations in several variables. New York: Academic Press 1970."},{"key":"BF02246758_CR21","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1017\/S0305004100030401","volume":"51","author":"R. Penrose","year":"1955","unstructured":"Penrose, R.: A generalized inverse for matrices. Proc. Cambridge Philos. Soc.51, 406\u2013413 (1955).","journal-title":"Proc. Cambridge Philos. Soc."},{"key":"BF02246758_CR22","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1093\/comjnl\/13.3.309","volume":"13","author":"J. Peters","year":"1970","unstructured":"Peters, J., Wilkinson, J.: The least squares problem and pseudo-inverses. Comp. J.13, 309\u2013316 (1970).","journal-title":"Comp. J."},{"key":"BF02246758_CR23","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1007\/BF01932400","volume":"17","author":"H. Ramsin","year":"1977","unstructured":"Ramsin, H., Wedin, P. A.: A comparison of some algorithms for the nonlinear least squares problem. BIT17, 72\u201390 (1977).","journal-title":"BIT"},{"key":"BF02246758_CR24","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1137\/0718079","volume":"18","author":"N. Villiers de","year":"1981","unstructured":"Villiers, N. de, Glasser, D.: A continuation method for nonlinear regression. SIAM J. Numer. Anal.18, 1139\u20131154 (1981).","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02246758_CR25","volume-title":"Continuation methods","year":"1979","unstructured":"Wacker, Hj. (ed.): Continuation methods. New York: Academic Press 1979."},{"key":"BF02246758_CR26","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1007\/BF01934400","volume":"22","author":"T. J. Ypma","year":"1982","unstructured":"Ypma, T. J.: Affine invariant convergence results for Newton's Method. BIT22, 108\u2013118 (1982).","journal-title":"BIT"}],"container-title":["Computing"],"original-title":[],"language":"de","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02246758.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02246758\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02246758","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T10:30:25Z","timestamp":1558002625000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02246758"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,12]]},"references-count":26,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1982,12]]}},"alternative-id":["BF02246758"],"URL":"https:\/\/doi.org\/10.1007\/bf02246758","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,12]]}}}