An Algorithm for Least-Squares Estimation of Nonlinear Parameters

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Previous article Next article An Algorithm for Least-Squares Estimation of Nonlinear ParametersDonald W. MarquardtDonald W. Marquardthttps://doi.org/10.1137/0111030PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] G. W. Booth, , G. E. P. Box, , M. E. Muller and , T. I. Peterson, Forecasting by Generalized Regression Methods, Nonlinear Estimation (Princeton—IBM), Mimeo. (IBM Share Program No. 687 WL NL1), International Business Machines Corp., 1959 Google Scholar[2] G. E. P. Box and , G. A. Coutie, Application of digital computers in the exploration of functional relationships, Proc. Inst. Elec. Engrs. B, 103 (1957), 100–107 MR0094906 Google Scholar[3] Haskell B. Curry, The method of steepest descent for non-linear minimization problems, Quart. Appl. Math., 2 (1944), 258–261 MR0010667 0061.26801 CrossrefGoogle Scholar[4] H. O. Hartley, The modified Gauss-Newton method for the fitting of non-linear regression functions by least squares, Technometrics, 3 (1961), 269–280 MR0124117 0096.34603 CrossrefISIGoogle Scholar[5] D. W. Marquardt, , Chem. Eng. Progr., 55 (1959), 65–70 Google Scholar[6] D. W. Marquardt, , R. G. Bennett and , E. J. Burrell, , Jour. Molec. Spectroscopy, 7 (1961), 269–279 10.1016/0022-2852(61)90360-5 CrossrefISIGoogle Scholar[7] D. D. Morrison, Methods for nonlinear least squares problems and convergence proofs, Tracking Programs and Orbit Determination, Proc. Jet Propulsion Laboratory Seminar, 1960, 1–9 Google Scholar[8] Kenneth Levenberg, A method for the solution of certain non-linear problems in least squares, Quart. Appl. Math., 2 (1944), 164–168 MR0010666 0063.03501 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Shadowing-Based Data Assimilation Method for Partially Observed ModelsBart M. de Leeuw and Svetlana DubinkinaSIAM Journal on Applied Dynamical Systems, Vol. 21, No. 2 | 11 April 2022AbstractPDF (2268 KB)Localized Sensitivity Analysis at High-Curvature Boundary Points of Reconstructing Inclusions in Transmission ProblemsHabib Ammari, Yat Tin Chow, and Hongyu LiuSIAM Journal on Mathematical Analysis, Vol. 54, No. 2 | 9 March 2022AbstractPDF (829 KB)A Stochastic Levenberg--Marquardt Method Using Random Models with Complexity ResultsEl Houcine Bergou, Youssef Diouane, Vyacheslav Kungurtsev, and Clément W. RoyerSIAM/ASA Journal on Uncertainty Quantification, Vol. 10, No. 1 | 29 March 2022AbstractPDF (616 KB)Derivative-Free Bayesian Inversion Using Multiscale DynamicsG. A. Pavliotis, A. M. Stuart, and U. 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range:pp. 431-441ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics