scholarly journals A new sufficient condition for the well-posedness of non-linear least square problems arising in identification and control

2008 ◽  
pp. 452-463 ◽  
Author(s):  
Guy Chavent
Keyword(s):  
Least Square ◽  
Well Posedness ◽  
Sufficient Condition ◽  
Non Linear ◽  
Linear Least Square ◽  
And Control ◽  
Least Square Problems

scholarly journals A Bayesian hierarchical model for demand curve analysis

2016 ◽  
Vol 27 (7) ◽  
pp. 2038-2049
Author(s):  
Yen-Yi Ho ◽  
Tien Nhu Vo ◽  
Haitao Chu ◽  
Xianghua Luo ◽  
Chap T Le
Keyword(s):  
Hierarchical Model ◽  
Demand Curve ◽  
Bayesian Hierarchical Model ◽  
Curve Analysis ◽  
Least Square ◽  
Self Administration ◽  
Bayesian Hierarchical ◽  
Least Square Regression ◽  
Non Linear ◽  
Linear Least Square

Drug self-administration experiments are a frequently used approach to assessing the abuse liability and reinforcing property of a compound. It has been used to assess the abuse liabilities of various substances such as psychomotor stimulants and hallucinogens, food, nicotine, and alcohol. The demand curve generated from a self-administration study describes how demand of a drug or non-drug reinforcer varies as a function of price. With the approval of the 2009 Family Smoking Prevention and Tobacco Control Act, demand curve analysis provides crucial evidence to inform the US Food and Drug Administration’s policy on tobacco regulation, because it produces several important quantitative measurements to assess the reinforcing strength of nicotine. The conventional approach popularly used to analyze the demand curve data is individual-specific non-linear least square regression. The non-linear least square approach sets out to minimize the residual sum of squares for each subject in the dataset; however, this one-subject-at-a-time approach does not allow for the estimation of between- and within-subject variability in a unified model framework. In this paper, we review the existing approaches to analyze the demand curve data, non-linear least square regression, and the mixed effects regression and propose a new Bayesian hierarchical model. We conduct simulation analyses to compare the performance of these three approaches and illustrate the proposed approaches in a case study of nicotine self-administration in rats. We present simulation results and discuss the benefits of using the proposed approaches.

Non-Linear Least Squares Large Misalignment Estimation in Transfer Alignment

2014 ◽  
Vol 989-994 ◽  
pp. 1962-1968 ◽  
Author(s):  
Yuan Lu ◽  
Xiang Hong Cheng
Keyword(s):  
Trust Region Method ◽  
Estimation Method ◽  
Trust Region ◽  
Least Square ◽  
Linear Filtering ◽  
Linear Least Squares ◽  
Transfer Alignment ◽  
Non Linear ◽  
Simulation Results ◽  
Linear Least Square

Large misalignment is unavoidable for subsystems which could be deployed randomly on the carriers such as shipborne aircrafts, AUV. Ordinary linear filtering algorithms don’t converge fast and accurately in non-linear conditions. It's critical for the accuracy of the transfer alignment. In this paper, a new misalignment and gyroscope bias online estimation method based on angular velocity processing is presented. Sensor measurements of M-SINS and S-SINS will be recorded for a certain period. Misalignment and the gyroscope bias will be calculated from these measurements directly with non-linear least square algorithm. Trust region method with pre-conditioning, subspace and conjugate gradient are applied for faster converge and better accuracy. Simulation results demonstrate the effectiveness of the algorithm.

APPLICATION OF NON-LINEAR LEAST SQUARE METHOD TO ESTIMATE THE MUSCLE DYNAMICS OF THE ELBOW JOINT

2006 ◽  
Vol 39 (1) ◽  
pp. 1168-1173 ◽  
Author(s):  
Gentiane Venture ◽  
Yoshihiko Nakamura ◽  
Katsu Yamane
Keyword(s):  
Elbow Joint ◽  
Least Square Method ◽  
Least Square ◽  
Muscle Dynamics ◽  
Non Linear ◽  
Linear Least Square

scholarly journals Calculation of ICG kinetics by two simultaneous differential equations and non-linear least square method.

Kanzo ◽  
1988 ◽  
Vol 29 (10) ◽  
pp. 1368-1373
Author(s):  
Yutaka SAGAWA ◽  
Toshiko YOSHIKATA ◽  
Nagaki SHIMADA ◽  
Motonobu SUGIMOTO
Keyword(s):  
Differential Equations ◽  
Least Square Method ◽  
Least Square ◽  
Non Linear ◽  
Linear Least Square

scholarly journals Comparison Results on Preconditioned GAOR Methods for Weighted Linear Least Squares Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Guangbin Wang ◽  
Yanli Du ◽  
Fuping Tan
Keyword(s):  
Least Squares ◽  
Least Square ◽  
Linear Least Squares ◽  
Least Squares Problems ◽  
Numerical Example ◽  
Comparison Results ◽  
Linear Least Squares Problems ◽  
Linear Least Square ◽  
Least Square Problems ◽  
Theoretical Results

We present preconditioned generalized accelerated overrelaxation methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GAOR methods converge faster than the GAOR method whenever the GAOR method is convergent. Finally, we give a numerical example to confirm our theoretical results.

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