Nonlinear-Least-Squares Analysis of Slow-Motion EPR Spectra in One and Two Dimensions Using a Modified Levenberg–Marquardt Algorithm

1996 ◽  
Vol 120 (2) ◽  
pp. 155-189 ◽  
Author(s):  
David E. Budil ◽  
Sanghyuk Lee ◽  
Sunil Saxena ◽  
Jack H. Freed
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Slow Motion ◽  
Two Dimensions ◽  
Epr Spectra ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt

Modified inexact Levenberg–Marquardt methods for solving nonlinear least squares problems

2019 ◽  
Vol 74 (2) ◽  
pp. 547-582 ◽  
Author(s):  
Jifeng Bao ◽  
Carisa Kwok Wai Yu ◽  
Jinhua Wang ◽  
Yaohua Hu ◽  
Jen-Chih Yao
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Least Squares Problems ◽  
Levenberg Marquardt

scholarly journals Parameter identification for symbolic regression using nonlinear least squares

2019 ◽  
Vol 21 (3) ◽  
pp. 471-501 ◽  
Author(s):  
Michael Kommenda ◽  
Bogdan Burlacu ◽  
Gabriel Kronberger ◽  
Michael Affenzeller
Keyword(s):  
Genetic Programming ◽  
Local Search ◽  
Parameter Identification ◽  
Least Squares ◽  
Automatic Differentiation ◽  
Nonlinear Least Squares ◽  
Symbolic Regression ◽  
Machine Learning Algorithms ◽  
Benchmark Problems ◽  
Marquardt Algorithm

AbstractIn this paper we analyze the effects of using nonlinear least squares for parameter identification of symbolic regression models and integrate it as local search mechanism in tree-based genetic programming. We employ the Levenberg–Marquardt algorithm for parameter optimization and calculate gradients via automatic differentiation. We provide examples where the parameter identification succeeds and fails and highlight its computational overhead. Using an extensive suite of symbolic regression benchmark problems we demonstrate the increased performance when incorporating nonlinear least squares within genetic programming. Our results are compared with recently published results obtained by several genetic programming variants and state of the art machine learning algorithms. Genetic programming with nonlinear least squares performs among the best on the defined benchmark suite and the local search can be easily integrated in different genetic programming algorithms as long as only differentiable functions are used within the models.

Determining Extrinsic Parameters for Active Stereovision

2009 ◽  
Vol 13 (2) ◽  
pp. 76-79 ◽  
Author(s):  
Huawei Wang ◽  
◽  
De Xu
Keyword(s):  
Least Squares ◽  
Rotational Axis ◽  
The Novel ◽  
Mapping Model ◽  
Least Squares Fitting ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Extrinsic Parameters ◽  
Novel Method ◽  
The Relationship

In the novel method we propose for determining extrinsic parameters for active stereovision, we first map the relationship between rotational and yaw angles based on least squares fitting, then optimize the rotational axis between two cameras using the Levenberg-Marquardt algorithm. Extrinsic parameters are then easily derived for active stereovision based on the mapping model without complex recalibration. The results of experiments confirmed our proposed method's feasibility.

scholarly journals Hybrid Levenberg–Marquardt and weak-constraint ensemble Kalman smoother method

2016 ◽  
Vol 23 (2) ◽  
pp. 59-73 ◽  
Author(s):  
J. Mandel ◽  
E. Bergou ◽  
S. Gürol ◽  
S. Gratton ◽  
I. Kasanický
Keyword(s):  
Least Squares ◽  
Newton Method ◽  
Nonlinear Least Squares ◽  
Additional Observation ◽  
Linear Least Squares ◽  
Regularization Term ◽  
Marquardt Method ◽  
Kalman Smoother ◽  
Levenberg Marquardt ◽  
Adjoint Operators

Abstract. The ensemble Kalman smoother (EnKS) is used as a linear least-squares solver in the Gauss–Newton method for the large nonlinear least-squares system in incremental 4DVAR. The ensemble approach is naturally parallel over the ensemble members and no tangent or adjoint operators are needed. Furthermore, adding a regularization term results in replacing the Gauss–Newton method, which may diverge, by the Levenberg–Marquardt method, which is known to be convergent. The regularization is implemented efficiently as an additional observation in the EnKS. The method is illustrated on the Lorenz 63 model and a two-level quasi-geostrophic model.

scholarly journals Hybrid Levenberg–Marquardt and weak constraint ensemble Kalman smoother method

2015 ◽  
Vol 2 (3) ◽  
pp. 865-902 ◽  
Author(s):  
J. Mandel ◽  
E. Bergou ◽  
S. Gürol ◽  
S. Gratton
Keyword(s):  
Least Squares ◽  
Newton Method ◽  
Nonlinear Least Squares ◽  
Additional Observation ◽  
Linear Least Squares ◽  
Regularization Term ◽  
Marquardt Method ◽  
Kalman Smoother ◽  
Levenberg Marquardt ◽  
Adjoint Operators

Abstract. We propose to use the ensemble Kalman smoother (EnKS) as the linear least squares solver in the Gauss–Newton method for the large nonlinear least squares in incremental 4DVAR. The ensemble approach is naturally parallel over the ensemble members and no tangent or adjoint operators are needed. Further, adding a regularization term results in replacing the Gauss–Newton method, which may diverge, by the Levenberg–Marquardt method, which is known to be convergent. The regularization is implemented efficiently as an additional observation in the EnKS. The method is illustrated on the Lorenz 63 and the two-level quasi-geostrophic model problems.

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