An Algorithm for Least-Squares Estimation of Nonlinear Parameters
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
G. W. Booth, G. E. P. Box, M. E. Muller, 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
2.
G. E. P. Box, G. A. Coutie, Application of digital computers in the exploration of functional relationships, Proc. Inst. Elec. Engrs. B, 103 (1957), 100–107
3.
Haskell B. Curry, The method of steepest descent for non-linear minimization problems, Quart. Appl. Math., 2 (1944), 258–261
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
5.
D. W. Marquardt, Chem. Eng. Progr., 55 (1959), 65–70
6.
D. W. Marquardt, R. G. Bennett, E. J. Burrell, Jour. Molec. Spectroscopy, 7 (1961), 269–279
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
8.
Kenneth Levenberg, A method for the solution of certain non-linear problems in least squares, Quart. Appl. Math., 2 (1944), 164–168
Information & Authors
Information
Published In
Copyright
Copyright © 1963 Society for Industrial and Applied Mathematics.
History
Submitted: 13 June 1962
Published online: 13 July 2006
Authors
Metrics & Citations
Metrics
Citations
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited By
- Regularized Newton Method with Global \({\boldsymbol{\mathcal{O}(1/{k}^2)}}\) ConvergenceSIAM Journal on Optimization, Vol. 33, No. 3 | 14 July 2023
- Inverse Problems for Subdiffusion from Observation at an Unknown Terminal TimeSIAM Journal on Applied Mathematics, Vol. 83, No. 4 | 17 July 2023
- An Optimized Dynamic Mode Decomposition Model Robust to Multiplicative NoiseSIAM Journal on Applied Dynamical Systems, Vol. 22, No. 1 | 16 February 2023
- Shadowing-Based Data Assimilation Method for Partially Observed ModelsSIAM Journal on Applied Dynamical Systems, Vol. 21, No. 2 | 11 April 2022
- Localized Sensitivity Analysis at High-Curvature Boundary Points of Reconstructing Inclusions in Transmission ProblemsSIAM Journal on Mathematical Analysis, Vol. 54, No. 2 | 9 March 2022
- A Stochastic Levenberg--Marquardt Method Using Random Models with Complexity ResultsSIAM/ASA Journal on Uncertainty Quantification, Vol. 10, No. 1 | 29 March 2022
- Derivative-Free Bayesian Inversion Using Multiscale DynamicsSIAM Journal on Applied Dynamical Systems, Vol. 21, No. 1 | 24 January 2022
- Back MatterFundamentals of Numerical Computation: Julia Edition | 6 July 2023
- Convergence of Newton-MR under Inexact Hessian InformationSIAM Journal on Optimization, Vol. 31, No. 1 | 7 January 2021
- A Nonmonotone Matrix-Free Algorithm for Nonlinear Equality-Constrained Least-Squares ProblemsSIAM Journal on Scientific Computing, Vol. 43, No. 5 | 13 September 2021
- On the Quadratic Convergence of the Cubic Regularization Method under a Local Error Bound ConditionSIAM Journal on Optimization, Vol. 29, No. 1 | 28 March 2019
- Random Sampling from Joint Probability Distributions Defined in a Bayesian FrameworkSIAM Journal on Scientific Computing, Vol. 41, No. 1 | 15 January 2019
- The Conjugate Residual Method in Linesearch and Trust-Region MethodsSIAM Journal on Optimization, Vol. 29, No. 3 | 25 July 2019
- Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and OptimizationSIAM Review, Vol. 60, No. 3 | 8 August 2018
- Iterative Importance Sampling Algorithms for Parameter EstimationSIAM Journal on Scientific Computing, Vol. 40, No. 2 | 1 March 2018
- A Duality-Based Optimization Approach for Model Adaptivity in Heterogeneous Multiscale ProblemsMultiscale Modeling & Simulation, Vol. 16, No. 1 | 1 March 2018
- Newton Correction Methods for Computing Real Eigenpairs of Symmetric TensorsSIAM Journal on Matrix Analysis and Applications, Vol. 39, No. 3 | 3 July 2018
- Variable Projection Methods for an Optimized Dynamic Mode DecompositionSIAM Journal on Applied Dynamical Systems, Vol. 17, No. 1 | 1 February 2018
- An ODE-Based Method for Computing the Distance of Coprime Polynomials to Common DivisibilitySIAM Journal on Numerical Analysis, Vol. 55, No. 3 | 22 June 2017
- The Use of Quadratic Regularization with a Cubic Descent Condition for Unconstrained OptimizationSIAM Journal on Optimization, Vol. 27, No. 2 | 6 June 2017
- Levenberg--Marquardt Methods Based on Probabilistic Gradient Models and Inexact Subproblem Solution, with Application to Data AssimilationSIAM/ASA Journal on Uncertainty Quantification, Vol. 4, No. 1 | 16 August 2016
- Synchronization of Independently Moving Cameras via Motion RecoverySIAM Journal on Imaging Sciences, Vol. 9, No. 3 | 7 July 2016
- An Efficient Gauss--Newton Algorithm for Symmetric Low-Rank Product Matrix ApproximationsSIAM Journal on Optimization, Vol. 25, No. 3 | 6 August 2015
- Factorization Approach to Structured Low-Rank Approximation with ApplicationsSIAM Journal on Matrix Analysis and Applications, Vol. 35, No. 3 | 11 September 2014
- An Algebraic Solution for the Candecomp/PARAFAC Decomposition with Circulant FactorsSIAM Journal on Matrix Analysis and Applications, Vol. 35, No. 4 | 11 December 2014
- Structured Low-Rank Approximation with Missing DataSIAM Journal on Matrix Analysis and Applications, Vol. 34, No. 2 | 27 June 2013
- Rank-Deficient Nonlinear Least Squares Problems and Subset SelectionSIAM Journal on Numerical Analysis, Vol. 49, No. 3 | 23 June 2011
- Computing Points that Satisfy Second Order Necessary Optimality Conditions for Unconstrained MinimizationSIAM Journal on Optimization, Vol. 20, No. 4 | 19 February 2010
- On the Convergence of Recursive Trust-Region Methods for Multiscale Nonlinear Optimization and Applications to Nonlinear MechanicsSIAM Journal on Numerical Analysis, Vol. 47, No. 4 | 4 September 2009
- Relative Periodic Solutions of the Complex Ginzburg--Landau EquationSIAM Journal on Applied Dynamical Systems, Vol. 4, No. 4 | 7 August 2006
- Linear versus Nonlinear Dimensionality Reduction of High-Dimensional Dynamical SystemsSIAM Journal on Scientific Computing, Vol. 25, No. 6 | 25 July 2006
- Analyzing the Dynamics of Cellular Flames Using Karhunen--Loève Decomposition and Autoassociative Neural NetworksSIAM Journal on Scientific Computing, Vol. 24, No. 5 | 25 July 2006
- An Elementary Model for Control of a Semiconductor Etching ProcessSIAM Review, Vol. 44, No. 4 | 4 August 2006
- A Trust-Region Approach to Nonlinear Systems of Equalities and InequalitiesSIAM Journal on Optimization, Vol. 9, No. 2 | 31 July 2006
- A Global Convergence Theory for Dennis, El-Alem, and Maciel's Class of Trust-Region Algorithms for Constrained Optimization without Assuming RegularitySIAM Journal on Optimization, Vol. 9, No. 4 | 31 July 2006
- Convergence Properties of Minimization Algorithms for Convex Constraints Using a Structured Trust RegionSIAM Journal on Optimization, Vol. 6, No. 4 | 31 July 2006
- Restricted Step and Levenberg–Marquardt Techniques in Proximal Bundle Methods for Nonconvex Nondifferentiable OptimizationSIAM Journal on Optimization, Vol. 6, No. 1 | 31 July 2006
- A Parallel Nonlinear Least-Squares Solver: Theoretical Analysis and Numerical ResultsSIAM Journal on Scientific and Statistical Computing, Vol. 13, No. 3 | 13 July 2006
- The Early Use of Matrix Diagonal Increments in Statistical ProblemsSIAM Review, Vol. 31, No. 3 | 18 July 2006
- Nonstandard Scaling Matrices for Trust Region Gauss–Newton MethodsSIAM Journal on Scientific and Statistical Computing, Vol. 10, No. 4 | 13 July 2006
- A Continuation Approach for Solving Large-Residual Nonlinear Least Squares ProblemsSIAM Journal on Scientific and Statistical Computing, Vol. 8, No. 4 | 14 July 2006
- The Use of Linear Programming for the Solution of Sparse Sets of Nonlinear EquationsSIAM Journal on Scientific and Statistical Computing, Vol. 8, No. 2 | 14 July 2006
- Newton’s Method with a Model Trust Region ModificationSIAM Journal on Numerical Analysis, Vol. 19, No. 2 | 17 July 2006
- Computing Optimal Locally Constrained StepsSIAM Journal on Scientific and Statistical Computing, Vol. 2, No. 2 | 16 May 2012
- Robust Methods for Solving Systems of Nonlinear EquationsSIAM Journal on Scientific and Statistical Computing, Vol. 1, No. 1 | 16 May 2012
- Some Problems in the Control of Distributed Systems, and Their Numerical SolutionSIAM Journal on Control and Optimization, Vol. 17, No. 1 | 18 July 2006
- Minimum Principles for Ill-Posed ProblemsSIAM Journal on Mathematical Analysis, Vol. 9, No. 4 | 17 February 2012
- Approximation to Data by Splines with Free KnotsSIAM Journal on Numerical Analysis, Vol. 15, No. 2 | 14 July 2006
- Dynamic Optimal Control Models in Advertising: a SurveySIAM Review, Vol. 19, No. 4 | 17 February 2012
- Use of Smoothing and Damping Techniques in the Solution of Nonlinear EquationsSIAM Review, Vol. 19, No. 1 | 18 July 2006
- Nonlinear Mean-Square Approximation of Finite SetsSIAM Journal on Numerical Analysis, Vol. 12, No. 1 | 14 July 2006
- Complex Linear Least SquaresSIAM Review, Vol. 15, No. 4 | 18 July 2006
- Multivariate Splines with Nondegenerate PartitionsSIAM Journal on Numerical Analysis, Vol. 10, No. 4 | 14 July 2006
- Parameter Selection for Modified Newton Methods for Function MinimizationSIAM Journal on Numerical Analysis, Vol. 7, No. 3 | 14 July 2006
- An Accelerated Gradient Projection Method for Linearly Constrained Nonlinear EstimationSIAM Journal on Applied Mathematics, Vol. 18, No. 2 | 1 August 2006
- Comparison of Gradient Methods for the Solution of Nonlinear Parameter Estimation ProblemsSIAM Journal on Numerical Analysis, Vol. 7, No. 1 | 14 July 2006
- A Survey of Numerical Methods for Unconstrained OptimizationSIAM Review, Vol. 12, No. 1 | 18 July 2006
- On a Theorem Used in Nonlinear Least SquaresSIAM Journal on Applied Mathematics, Vol. 14, No. 5 | 13 July 2006
- On the Stationary Values of a Second-Degree Polynomial on the Unit SphereJournal of the Society for Industrial and Applied Mathematics, Vol. 13, No. 4 | 13 July 2006