A nonlinear least squares data fitting problem arising in microwave measurement

1990 ◽  
pp. 458-465
Author(s):  
M. G. Cox ◽  
H. M. Jones
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Data Fitting ◽  
Microwave Measurement ◽  
Fitting Problem

Nonlinear least-squares data fitting in Excel spreadsheets

2010 ◽  
Vol 5 (2) ◽  
pp. 267-281 ◽  
Author(s):  
Gerdi Kemmer ◽  
Sandro Keller
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Data Fitting ◽  
Fitting In

Powell’s method-based nonlinear least-squares data fitting for the Mittag-Leffler relaxation function

2015 ◽  
Vol 22 (5) ◽  
pp. 1058-1067
Author(s):  
Changqing Fang ◽  
Huiyu Sun ◽  
Jianping Gu
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Relaxation Function ◽  
Nonlinear Least Squares ◽  
Data Fitting ◽  
Direct Search ◽  
Search Method ◽  
Direct Search Method ◽  
Viscoelastic Models

The Mittag-Leffler relaxation function, [Formula: see text], with [Formula: see text], plays an important role in the fractional viscoelastic models. The Mittag-Leffler function is an infinite series whose analytic derivatives are unexplored, thus a direct search method based on Powell’s method is introduced to solve the minimization problem of nonlinear least-squares data fitting for Mittag-Leffler relaxation function in this paper. A simple and effective method is provided for the determination of the initial values and an acceleration strategy is proposed for this direct search method. Numerical results show this direct search method is efficient in the parameter estimation of the Mittag-Leffler relaxation function. Furthermore, the acceleration strategy proves to be conducive to improving the computational efficiency of this direct search method.

scholarly journals Efficient Parameters Estimation Method for the Separable Nonlinear Least Squares Problem

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Ke Wang ◽  
Guolin Liu ◽  
Qiuxiang Tao ◽  
Min Zhai
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Nonlinear Least Squares ◽  
Coefficient Matrix ◽  
Nonlinear Parameters ◽  
Nonlinear Least Squares Problem ◽  
Ill Posed ◽  
Characteristic Values ◽  
Parameter Separation ◽  
Fitting Problem

In this work, we combine the special structure of the separable nonlinear least squares problem with a variable projection algorithm based on singular value decomposition to separate linear and nonlinear parameters. Then, we propose finding the nonlinear parameters using the Levenberg–Marquart (LM) algorithm and either solve the linear parameters using the least squares method directly or by using an iteration method that corrects the characteristic values based on the L-curve, according to whether or not the nonlinear function coefficient matrix is ill posed. To prove the feasibility of the proposed method, we compared its performance on three examples with that of the LM method without parameter separation. The results show that (1) the parameter separation method reduces the number of iterations and improves computational efficiency by reducing the parameter dimensions and (2) when the coefficient matrix of the linear parameters is well-posed, using the least squares method to solve the fitting problem provides the highest fitting accuracy. When the coefficient matrix is ill posed, the method of correcting characteristic values based on the L-curve provides the most accurate solution to the fitting problem.

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