A COMPARISON OF OPTIMIZATION METHODS FOR FITTING CURVES TO INFRARED BAND ENVELOPES

1966 ◽  
Vol 44 (24) ◽  
pp. 3031-3050 ◽  
Author(s):  
J. Pitha ◽  
R. Norman Jones
Keyword(s):  
Least Squares ◽  
Computation Time ◽  
Direct Methods ◽  
Nonlinear Least Squares ◽  
Optimization Methods ◽  
Infrared Band ◽  
Band Shape ◽  
Analytical Functions ◽  
Degree Of Convergence ◽  
Better Than

A comparison has been made of seven numerical methods of fitting infrared absorption band envelopes with analytical functions using nonlinear least squares approximations. Gauss and Cauchy (Lorentz) band shape functions are used, and also sum and product combinations of the two. The methods have been compared with respect to both the degree of convergence and to the computation time needed to achieve an acceptable fit.The most effective method has matched the overlap envelope of a steroid spectrum containing 16 bands; this necessitated the optimization of 65 variables. More complex spectra can be dealt with by a "moving subspace" modification in which only the parameters of a group of adjacent bands are adjusted at one time. Automatic computer programs have been written for five of the methods, and for the moving subspace modification. These will be published elsewhere.If the computed curve is convoluted with the spectral slit function before making the least squares calculations, the distortion of the observed spectrum caused by the finite spectral slit width can be corrected. In some cases this method of diminishing the slit distortion is better than direct methods, particularly when dealing with strongly overlapped bands.

scholarly journals DETECTING AN OBSTACLE IMMERSED IN A FLUID BY SHAPE OPTIMIZATION METHODS

2011 ◽  
Vol 21 (10) ◽  
pp. 2069-2101 ◽  
Author(s):  
MEHDI BADRA ◽  
FABIEN CAUBET ◽  
MARC DAMBRINE
Keyword(s):  
Shape Optimization ◽  
Least Squares ◽  
Stokes Equations ◽  
Neumann Boundary ◽  
Nonlinear Least Squares ◽  
Identification Problem ◽  
Optimization Methods ◽  
Riesz Operator ◽  
Shape Derivatives ◽  
Shape Hessian

The paper presents a theoretical study of an identification problem by shape optimization methods. The question is to detect an object immersed in a fluid. Here, the problem is modeled by the Stokes equations and treated as a nonlinear least-squares problem. We consider both the Dirichlet and Neumann boundary conditions. Firstly, we prove an identifiability result. Secondly, we prove the existence of the first-order shape derivatives of the state, we characterize them and deduce the gradient of the least-squares functional. Moreover, we study the stability of this setting. We prove the existence of the second-order shape derivatives and we give the expression of the shape Hessian. Finally, the compactness of the Riesz operator corresponding to this shape Hessian is shown and the ill-posedness of the identification problem follows. This explains the need of regularization to numerically solve this problem.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

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