Mueller Matrix Ellipsometer Based on Nonlinear Least Squares Fitting Method

2013 ◽  
Vol 40 (4) ◽  
pp. 0408004
Author(s):  
侯俊峰 Hou Junfeng ◽  
王东光 Wang Dongguang ◽  
邓元勇 Deng Yuanyong ◽  
孙英姿 Sun Yingzi ◽  
张志勇 Zhang Zhiyong
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Mueller Matrix ◽  
Least Squares Fitting ◽  
Fitting Method

scholarly journals Methods for Fitting the Limit State Function of the Residual Strength of Damaged Ships

2022 ◽  
Vol 10 (1) ◽  
pp. 102
Author(s):  
Zhiyao Zhu ◽  
Huilong Ren ◽  
Xiuhuan Wang ◽  
Nan Zhao ◽  
Chenfeng Li
Keyword(s):  
Least Squares ◽  
Residual Strength ◽  
Least Squares Method ◽  
Limit State ◽  
Nonlinear Least Squares ◽  
State Function ◽  
Limit State Function ◽  
Distribution Models ◽  
Sample Distribution ◽  
Fitting Method

The limit state function is important for the assessment of the longitudinal strength of damaged ships under combined bending moments in severe waves. As the limit state function cannot be obtained directly, the common approach is to calculate the results for the residual strength and approximate the limit state function by fitting, for which various methods have been proposed. In this study, four commonly used fitting methods are investigated: namely, the least-squares method, the moving least-squares method, the radial basis function neural network method, and the weighted piecewise fitting method. These fitting methods are adopted to fit the limit state functions of four typically sample distribution models as well as a damaged tanker and damaged bulk carrier. The residual strength of a damaged ship is obtained by an improved Smith method that accounts for the rotation of the neutral axis. Analysis of the results shows the accuracy of the linear least-squares method and nonlinear least-squares method, which are most commonly used by researchers, is relatively poor, while the weighted piecewise fitting method is the better choice for all investigated combined-bending conditions.

THE DECAY OF 89Rb

1966 ◽  
Vol 44 (11) ◽  
pp. 2661-2683 ◽  
Author(s):  
J. E. Kitching ◽  
M. W. Johns
Keyword(s):  
Least Squares ◽  
Gamma Rays ◽  
Nonlinear Least Squares ◽  
Q Value ◽  
Least Squares Fitting

The decay of 14.9-minute 89Rb to levels in 89Sr has been studied by use of Ge(Li) detectors, NaI(Tl) detectors, and a magnetic beta-ray spectrometer. Fourteen gamma rays have been studied by γ−γ and β−γ coincidence experiments and establish levels at 0, 1.031, 2.000, 2.277, 2.567, 2.708, 2.770, 3.225, and 3.500 MeV. The Q value is 4.486 ± 0.012 MeV. The γ−γ and β−γ data were analyzed by a nonlinear least-squares fitting technique, which is described.

Application of Legendre Polynomial in Predicting Total Energy Consumption

2015 ◽  
Vol 713-715 ◽  
pp. 1627-1630
Author(s):  
Hong Qin Zhang ◽  
Lai Bin Gao
Keyword(s):  
Energy Consumption ◽  
Total Energy ◽  
Least Squares ◽  
Legendre Polynomial ◽  
Statistical Data ◽  
Least Squares Method ◽  
Total Energy Consumption ◽  
Least Squares Fitting ◽  
Fitting Method

Based on statistical data of National Statistical Bureau of China, and given the least-squares fitting of Legendre polynomial, the data of total energy consumption from 1978 to 2012 is analyzed by least squares method and Legendre polynomial least squares method respectively. The results showed that Legendre polynomial least squares fitting method is excellent and the data of total energy consumption from 2013 to 2016 is predicted by this method.

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