{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T16:53:57Z","timestamp":1776358437177,"version":"3.51.2"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2007,5,23]],"date-time":"2007-05-23T00:00:00Z","timestamp":1179878400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2007,10,11]]},"DOI":"10.1007\/s10589-007-9047-7","type":"journal-article","created":{"date-parts":[[2007,5,23]],"date-time":"2007-05-23T15:21:07Z","timestamp":1179933667000},"page":"195-216","source":"Crossref","is-referenced-by-count":24,"title":["A recursive algorithm for nonlinear least-squares problems"],"prefix":"10.1007","volume":"38","author":[{"given":"A.","family":"Alessandri","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Cuneo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"Pagnan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Sanguineti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,5,23]]},"reference":[{"key":"9047_CR1","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316757","volume-title":"Nonlinear Regression and Its Applications","author":"D.M. Bates","year":"1988","unstructured":"Bates, D.M., Watts, D.G.: Nonlinear Regression and Its Applications. Wiley, New York (1988)"},{"key":"9047_CR2","volume-title":"Nonlinear Programming","author":"D.P. Bertsekas","year":"1999","unstructured":"Bertsekas, D.P.: Nonlinear Programming, 2nd edn. Athena Scientific, Belmont (1999)","edition":"2"},{"issue":"3","key":"9047_CR3","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1137\/S1052623494268522","volume":"6","author":"D.P. Bertsekas","year":"1996","unstructured":"Bertsekas, D.P.: Incremental least\u2013squares methods and the extended Kalman filter. SIAM J. Optim. 6(3), 807\u2013822 (1996)","journal-title":"SIAM J. Optim."},{"key":"9047_CR4","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/978-1-4615-5703-6_2","volume-title":"Nonlinear Modeling: Advanced Black-Box Techniques","author":"L.A. Feldkamp","year":"1998","unstructured":"Feldkamp, L.A., Prokhorov, D.V., Eagen, C.F., Yuan, F.: Enhanced multi-stream Kalman filter training for recurrent networks. In: Suykens, J., Vandewalle, J. (eds.) Nonlinear Modeling: Advanced Black-Box Techniques, pp. 29\u201353. Kluwer Academic, Dordrecht (1998)"},{"issue":"2","key":"9047_CR5","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1023\/A:1025703629626","volume":"26","author":"H. Moriyama","year":"2003","unstructured":"Moriyama, H., Yamashita, N., Fukushima, M.: The incremental Gauss\u2013Newton algorithm with adaptive stepsize rule. Comput. Optim. Appl. 26(2), 107\u2013141 (2003)","journal-title":"Comput. Optim. Appl."},{"issue":"2","key":"9047_CR6","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.spl.2003.11.020","volume":"67","author":"H. Shuhe","year":"2004","unstructured":"Shuhe, H.: Consistency for the least squares estimator in nonlinear regression model. Stat. Probab. Lett. 67(2), 183\u2013192 (2004)","journal-title":"Stat. Probab. Lett."},{"issue":"4","key":"9047_CR7","doi-asserted-by":"crossref","first-page":"714","DOI":"10.1109\/9.754809","volume":"44","author":"K. Reif","year":"1999","unstructured":"Reif, K., G\u00fcnter, S., Yaz, E., Unbehauen, R.: Stochastic stability of the discrete-time extended Kalman filter. IEEE Trans. Autom. Control 44(4), 714\u2013728 (1999)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"3","key":"9047_CR8","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.jco.2004.11.002","volume":"21","author":"V. K\u016frkov\u00e1","year":"2005","unstructured":"K\u016frkov\u00e1, V., Sanguineti, M.: Learning with generalization capability by kernel methods of bounded complexity. J. Complex. 21(3), 350\u2013367 (2005)","journal-title":"J. Complex."},{"key":"9047_CR9","doi-asserted-by":"crossref","first-page":"318","DOI":"10.7551\/mitpress\/5236.001.0001","volume-title":"Parallel Distributed Processing: Explorations in the Microstructures of Cognition, vol. I: Foundations","author":"D.E. Rumelhart","year":"1986","unstructured":"Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning internal representation by error propagation. In: Rumelhart, D.E., McClelland, J.L., PDP Research Group (eds.) Parallel Distributed Processing: Explorations in the Microstructures of Cognition, vol. I: Foundations, pp. 318\u2013362. MIT, Cambridge (1986)"},{"issue":"9","key":"9047_CR10","doi-asserted-by":"crossref","first-page":"1415","DOI":"10.1109\/5.58323","volume":"78","author":"B. Widrow","year":"1990","unstructured":"Widrow, B., Lehr, M.A.: 30 years of adaptive neural networks: perceptron, madaline, and backpropagation. Proc. IEEE 78(9), 1415\u20131442 (1990)","journal-title":"Proc. IEEE"},{"key":"9047_CR11","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611971323","volume-title":"Numerical Analysis: A Second Course","author":"J.M. Ortega","year":"1990","unstructured":"Ortega, J.M.: Numerical Analysis: A Second Course. SIAM, Philadelphia (1990). Reprint of the 1972 edition by Academic, Now York"},{"key":"9047_CR12","volume-title":"Stochastic Processes and Filtering Theory","author":"A.H. Jazwinski","year":"1970","unstructured":"Jazwinski, A.H.: Stochastic Processes and Filtering Theory. Academic, New York (1970)"},{"key":"9047_CR13","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1017\/S0962492900002919","volume":"8","author":"A. Pinkus","year":"1999","unstructured":"Pinkus, A.: Approximation theory of the MLP model in neural networks. Acta Numer. 8, 143\u2013196 (1999)","journal-title":"Acta Numer."},{"issue":"2","key":"9047_CR14","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1162\/neco.1991.3.2.246","volume":"3","author":"J. Park","year":"1991","unstructured":"Park, J., Sandberg, I.W.: Universal approximation using radial\u2013basis\u2013function networks. Neural Comput. 3(2), 246\u2013257 (1991)","journal-title":"Neural Comput."},{"issue":"4","key":"9047_CR15","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1109\/72.508935","volume":"7","author":"T. Heskes","year":"1996","unstructured":"Heskes, T., Wiegerinck, W.: A theoretical comparison of batch-mode, on-line, cyclic, and almost-cyclic learning. IEEE Trans. Neural Netw. 7(4), 919\u2013925 (1996)","journal-title":"IEEE Trans. Neural Netw."},{"key":"9047_CR16","volume-title":"Neural Network Toolbox\u2014User\u2019s Guide","author":"H. Demuth","year":"2000","unstructured":"Demuth, H., Beale, M.: Neural Network Toolbox\u2014User\u2019s Guide. The Math Works, Natick (2000)"},{"issue":"2","key":"9047_CR17","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1109\/9.250476","volume":"38","author":"B.M. Bell","year":"1993","unstructured":"Bell, B.M., Cathey, F.W.: The iterated Kalman filter update as a Gauss\u2013Newton method. IEEE Trans Autom. Control 38(2), 294\u2013297 (1993)","journal-title":"IEEE Trans Autom. Control"},{"key":"9047_CR18","volume-title":"Practical Methods of Optimization","author":"R. Fletcher","year":"1987","unstructured":"Fletcher, R.: Practical Methods of Optimization. Wiley, Chichester (1987)"},{"issue":"2","key":"9047_CR19","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1162\/neco.1992.4.2.141","volume":"4","author":"R. Battiti","year":"1992","unstructured":"Battiti, R.: First- and second-order methods for learning: between steepest descent and Newton\u2019s method. Neural Comput. 4(2), 141\u2013166 (1992)","journal-title":"Neural Comput."},{"issue":"5","key":"9047_CR20","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1016\/0893-6080(90)90006-7","volume":"3","author":"T. Tollenaere","year":"1990","unstructured":"Tollenaere, T.: SuperSAB: fast adaptive backpropagation with good scaling properties. Neural Netw. 3(5), 561\u2013573 (1990)","journal-title":"Neural Netw."},{"issue":"4","key":"9047_CR21","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/0893-6080(88)90003-2","volume":"1","author":"R.A. Jacobs","year":"1988","unstructured":"Jacobs, R.A.: Increased rates of convergence through learning rate adaption. Neural Netw. 1(4), 295\u2013307 (1988)","journal-title":"Neural Netw."},{"issue":"2","key":"9047_CR22","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1016\/0377-2217(96)00035-5","volume":"93","author":"J.W. Denton","year":"1996","unstructured":"Denton, J.W., Hung, M.S.: A comparison of nonlinear optimization methods for supervised learning in multilayer feedforward neural networks. Eur. J. Oper. Res. 93(2), 358\u2013368 (1996)","journal-title":"Eur. J. Oper. Res."},{"key":"9047_CR23","doi-asserted-by":"crossref","unstructured":"Stinchcombe, M., White, H.: Approximation and learning unknown mappings using multilayer feedforward networks with bounded weights. In: Proc. Int. Joint Conf. on Neural Networks IJCNN\u201990, pp. III7\u2013III16 (1990)","DOI":"10.1109\/IJCNN.1990.137817"},{"key":"9047_CR24","first-page":"133","volume-title":"Advances in Neural Information Processing Systems 1","author":"S. Singhal","year":"1989","unstructured":"Singhal, S., Wu, L.: Training multilayer perceptrons with the extended Kalman algorithm. In: Touretzky, D.S. (ed.) Advances in Neural Information Processing Systems 1, pp. 133\u2013140. Morgan Kaufmann, San Mateo (1989)"},{"issue":"6","key":"9047_CR25","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1109\/34.141559","volume":"14","author":"D.W. Ruck","year":"1992","unstructured":"Ruck, D.W., Rogers, S.K., Kabrisky, M., Maybeck, P.S., Oxley, M.E.: Comparative analysis of backpropagation and the extended Kalman filter for training multilayer perceptrons. IEEE Trans. Pattern Anal. Mach. Intell. 14(6), 686\u2013691 (1992)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"4","key":"9047_CR26","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1109\/78.127966","volume":"40","author":"Y. Iiguni","year":"1992","unstructured":"Iiguni, Y., Sakai, H., Tokumaru, H.: A real-time learning algorithm for a multilayered neural network based on the extended Kalman filter. IEEE Trans. Signal Process. 40(4), 959\u2013966 (1992)","journal-title":"IEEE Trans. Signal Process."},{"issue":"9","key":"9047_CR27","doi-asserted-by":"crossref","first-page":"1605","DOI":"10.1088\/0305-4470\/32\/9\/009","volume":"32","author":"B. Schottky","year":"1999","unstructured":"Schottky, B., Saad, D.: Statistical mechanics of EKF learning in neural networks. J. Phys. A: Math. Gen. 32(9), 1605\u20131621 (1999)","journal-title":"J. Phys. A: Math. Gen."},{"issue":"6","key":"9047_CR28","doi-asserted-by":"crossref","first-page":"1265","DOI":"10.1109\/72.963763","volume":"12","author":"K. Nishiyama","year":"2001","unstructured":"Nishiyama, K., Suzuki, K.: H \u221e-learning of layered neural networks. IEEE Trans. Neural Netw. 12(6), 1265\u20131277 (2001)","journal-title":"IEEE Trans. Neural Netw."},{"issue":"6","key":"9047_CR29","doi-asserted-by":"crossref","first-page":"1314","DOI":"10.1109\/72.963768","volume":"12","author":"C.-S. Leung","year":"2001","unstructured":"Leung, C.-S., Tsoi, A.-C., Chan, L.W.: Two regularizers for recursive least squared algorithms in feedforward multilayered neural networks. IEEE Trans. Neural Netw. 12(6), 1314\u20131332 (2001)","journal-title":"IEEE Trans. Neural Netw."},{"issue":"2","key":"9047_CR30","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1109\/72.991413","volume":"13","author":"A. Alessandri","year":"2002","unstructured":"Alessandri, A., Sanguineti, M., Maggiore, M.: Optimization-based learning with bounded error for feedforward neural networks. IEEE Trans. Neural Netw. 13(2), 261\u2013273 (2002)","journal-title":"IEEE Trans. Neural Netw."},{"key":"9047_CR31","unstructured":"Prechelt, L.: PROBEN 1\u2014A set of neural network benchmark problems and benchmarking rules. Tech. Rep. 21\/94, Fakult\u00e4t f\u00fcr Informatik, Universit\u00e4t Karlsruhe, Germany, September 1994, Anonymous FTP: \/pub\/papers\/techreports\/1994\/1994-21.ps.gzonftp.ira.uka.de"},{"key":"9047_CR32","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1126\/science.267326","volume":"197","author":"M.C. Mackey","year":"1977","unstructured":"Mackey, M.C., Glass, L.: Oscillation and chaos in physiological control systems. Science 197, 287\u2013289 (1977)","journal-title":"Science"},{"key":"9047_CR33","volume-title":"Inequalities","author":"G. Hardy","year":"1989","unstructured":"Hardy, G., Littlewood, J.E., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1989)"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-007-9047-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-007-9047-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-007-9047-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,22]],"date-time":"2020-04-22T07:41:44Z","timestamp":1587541304000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-007-9047-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,5,23]]},"references-count":33,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2007,10,11]]}},"alternative-id":["9047"],"URL":"https:\/\/doi.org\/10.1007\/s10589-007-9047-7","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,5,23]]}}}