Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

A modified tangent-gas approximation for two-dimensional steady flow

1958 ◽  
Vol 4 (6) ◽  
pp. 600-606 ◽  
Author(s):  
G. Power ◽  
P. Smith
Keyword(s):  
Least Squares ◽  
Steady Flow ◽  
Variational Approach ◽  
Least Squares Method ◽  
Two Dimensional ◽  
Subsonic Flows ◽  
Von Karman ◽  
Straight Line ◽  
Volume Relationship ◽  
Pressure Volume Relationship

A set of two-dimensional subsonic flows past certain cylinders is obtained using hodograph methods, in which the true pressure-volume relationship is replaced by various straight-line approximations. It is found that the approximation obtained by a least-squares method possibly gives best results. Comparison is made with values obtained by using the von Kármán-Tsien approximation and also with results obtained by the variational approach of Lush & Cherry (1956).

A Direct Least Squares Method for Camera Pose Estimation Based on Straight Line Segment Correspondences

2015 ◽  
Vol 35 (6) ◽  
pp. 0615003
Author(s):  
李鑫 Li Xin ◽  
张跃强 Zhang Yueqiang ◽  
刘进博 Liu Jinbo ◽  
张小虎 Zhang Xiaohu ◽  
于起峰 Yu Qifeng
Keyword(s):  
Least Squares ◽  
Pose Estimation ◽  
Line Segment ◽  
Least Squares Method ◽  
Straight Line Segment ◽  
Camera Pose Estimation ◽  
Straight Line ◽  
Camera Pose

CONTROL STRATEGIES FOR CHAOTIC NEUROMODULES

1996 ◽  
Vol 06 (04) ◽  
pp. 693-703 ◽  
Author(s):  
NICO STOLLENWERK ◽  
FRANK PASEMANN
Keyword(s):  
Least Squares ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Least Squares Method ◽  
Control Strategies ◽  
Nonlinear Least Squares ◽  
The Neural Network ◽  
One Step ◽  
Nonlinear Least Squares Method ◽  
The One

Different strategies for control of chaotic systems are discussed: The well known Ott-Grebogi-Yorke algorithm and two alternative algorithms based on least-squares minimisation of the one step future deviation. To compare their effectiveness in the neural network context they are applied to a minimal two neuron module with discrete chaotic dynamics. The best method with respect to calculation effort, to neural implementation, and to controlling properties is the nonlinear least squares method. Furthermore, it is observed in simulations that one can stabilise a whole periodic orbit by applying the control signals only to one of its periodic points, which lies in a distinguished region of phase space.

scholarly journals Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems

2008 ◽  
Vol 8 (2) ◽  
pp. 6409-6436 ◽  
Author(s):  
C. A. Cantrell
Keyword(s):  
Least Squares ◽  
Atmospheric Chemistry ◽  
Least Squares Method ◽  
Technical Note ◽  
Routine Practice ◽  
Data Sets ◽  
Straight Line ◽  
Sample Data ◽  
Straight Lines ◽  
Best Fit

Abstract. The representation of data, whether geophysical observations, numerical model output or laboratory results, by a best fit straight line is a routine practice in the geosciences and other fields. While the literature is full of detailed analyses of procedures for fitting straight lines to values with uncertainties, a surprising number of scientists blindly use the standard least squares method, such as found on calculators and in spreadsheet programs, that assumes no uncertainties in the x values. Here, the available procedures for estimating the best fit straight line to data, including those applicable to situations for uncertainties present in both the x and y variables, are reviewed. Representative methods that are presented in the literature for bivariate weighted fits are compared using several sample data sets, and guidance is presented as to when the somewhat more involved iterative methods are required, or when the standard least-squares procedure would be expected to be satisfactory. A spreadsheet-based template is made available that employs one method for bivariate fitting.

Three-parameter transmission gear-shifting schedule for improved fuel economy

2017 ◽  
Vol 232 (4) ◽  
pp. 521-533 ◽  
Author(s):  
Chengsheng Miao ◽  
Haiou Liu ◽  
Guoming G Zhu
Keyword(s):  
Least Squares ◽  
Fuel Economy ◽  
Least Squares Method ◽  
Test Procedure ◽  
Rolling Resistance ◽  
Resistance Coefficient ◽  
Recursive Least Squares ◽  
Moving Least Squares Method ◽  
Two Parameter ◽  
Transmission Gear

Traditionally the transmission gear-shifting schedule is based upon the throttle position and the vehicle (or engine) speed. This paper proposes to add a third parameter, called the terrain coefficient, to form a three-parameter gear-shifting schedule for improving the fuel economy of a vehicle. The terrain coefficient is a compound parameter consisting of the road grade and the rolling resistance coefficient. It can be estimated in real time by the proposed multi-step recursive least-squares method. The dynamic programming and the moving least-squares method are adopted to optimize the gear sequences and to generate the three-parameter gear-shifting schedule. The proposed gear-shifting schedule is evaluated against the traditional two-parameter gear-shifting schedule via Simulink simulations and on-road experiments using a heavy-duty vehicle. The simulation results for the Urban Dynamometer Driving Schedule and the US06 Supplemental Federal Test Procedure driving cycles show that the fuel economies of the proposed gear-shifting schedule are improved by 3.3% and 2.7% respectively over that of the traditional two-parameter schedule. The experimental results indicate that the three-parameter gear-shifting schedule improves the fuel economy by 3.5% over the traditional schedule with a satisfactory acceleration performance.

A statistical comparison of parameter estimation for the Michaelis–Menten kinetics of human placental hexosaminidase

1985 ◽  
Vol 63 (3) ◽  
pp. 225-230 ◽  
Author(s):  
R. Tommasini ◽  
L. Endrenyi ◽  
P. A. Taylor ◽  
D. J. Mahuran ◽  
J. A. Lowden
Keyword(s):  
Least Squares ◽  
Kinetic Parameters ◽  
Least Squares Method ◽  
Nonlinear Least Squares ◽  
Linear Plot ◽  
Experimental Errors ◽  
Nonlinear Least Squares Method ◽  
Relative Errors ◽  
The One ◽  
Burk Plot

To enable the most effective method of kinetic discrimination between a group of isozymes such as those of human placental hexosaminidases (HEX), three methods estimating the parameters of the Michaelis–Menten equation were evaluated. Computer-simulated experiments were performed under various conditions. They indicated that, in the presence of constant absolute or relative errors, the method of unweighted nonlinear least squares yielded slightly more precise and accurate parameters than the method of the direct linear plot. Parameters calculated from the Lineweaver–Burk plot were very imprecise and inaccurate. The direct linear plot was comparatively resistant to outlier observations; however, only when outliers were substantial did the method become superior to nonlinear least squares. The calculation of a confidence limit is necessary for the evaluation of any resulting differences in the kinetic parameters for a set of isozymes. This can easily be calculated from either the Lineweaver–Burk plot or the nonlinear least-squares method. However, those calculated from the Lineweaver–Burk plot are biased, especially at higher levels of experimental errors. Therefore, the nonlinear least-squares method is the one most suited for the discrimination of a group of enzymes based on their kinetic parameters.

scholarly journals Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems

2008 ◽  
Vol 8 (17) ◽  
pp. 5477-5487 ◽  
Author(s):  
C. A. Cantrell
Keyword(s):  
Least Squares ◽  
Atmospheric Chemistry ◽  
Least Squares Method ◽  
Technical Note ◽  
Routine Practice ◽  
Data Sets ◽  
Straight Line ◽  
Sample Data ◽  
Straight Lines ◽  
Best Fit

Abstract. The representation of data, whether geophysical observations, numerical model output or laboratory results, by a best fit straight line is a routine practice in the geosciences and other fields. While the literature is full of detailed analyses of procedures for fitting straight lines to values with uncertainties, a surprising number of scientists blindly use the standard least-squares method, such as found on calculators and in spreadsheet programs, that assumes no uncertainties in the x values. Here, the available procedures for estimating the best fit straight line to data, including those applicable to situations for uncertainties present in both the x and y variables, are reviewed. Representative methods that are presented in the literature for bivariate weighted fits are compared using several sample data sets, and guidance is presented as to when the somewhat more involved iterative methods are required, or when the standard least-squares procedure would be expected to be satisfactory. A spreadsheet-based template is made available that employs one method for bivariate fitting.

ESTIMATION OF WEIBULL PARAMETERS USING A FUZZY LEAST-SQUARES METHOD

2004 ◽  
Vol 12 (05) ◽  
pp. 701-711 ◽  
Author(s):  
WEN-LIANG HUNG ◽  
YUAN-CHEN LIU
Keyword(s):  
Weibull Distribution ◽  
Least Squares ◽  
Robust Estimation ◽  
Least Squares Method ◽  
Estimation Method ◽  
Reliability Theory ◽  
Life Testing ◽  
Least Squares Algorithm ◽  
Two Parameter ◽  
Noise Cluster

The purpose of this paper is to find a robust estimation method for a two-parameter Weibull distribution when outliers are present. This is a relevant problem because of the usefulness of the Weibull distribution in life testing and reliability theory. For that purpose, a cluster-wise fuzzy least-squares algorithm with a noise cluster is used. This is because a noise cluster can be used for compensating the effects of outliers. Numerical comparisons between this fuzzy least-squares algorithm and the existing methods are implemented. According to these comparisons, it is suggested that the proposed fuzzy least-squares algorithm is preferable when the sample size is large.

Forecast and Control for the Amount of Rural Economic Crops

2014 ◽  
Vol 687-691 ◽  
pp. 4857-4860
Author(s):  
Wen Xi Duan
Keyword(s):  
Least Squares ◽  
Linear Function ◽  
Statistical Methods ◽  
Historical Data ◽  
Least Squares Method ◽  
The Real ◽  
Straight Line ◽  
Line Equation ◽  
And Control

The planting amount is determined by farmers according to the profit of planting economic crops. Moreover, the planting profit is estimated by using the statistical methods. The relation between the planting amount and the profit is similar to a linear function. However, the straight line equation has been set by using the historical data, calculating the slope of the straight line or adopting the least squares method. Therefore, the planting amount in next year will be calculated based on the equation. In a word, the planting amount in next year will be adjusted and controlled on the basis of the calculated planting amount and the real demand in the market.

scholarly journals Extended Peridynamics and Parameter Optimization Study Based on Moving Least Squares Method

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Jingwei Xu ◽  
Wei Hou ◽  
Shoucheng Luan ◽  
Shuting Mao ◽  
Guowei Liu ◽  
...  
Keyword(s):  
Weight Function ◽  
Least Squares ◽  
Least Squares Method ◽  
Moving Least Squares ◽  
Weight Functions ◽  
Optimization Study ◽  
Fitting Method ◽  
Moving Least Squares Method ◽  
Physical Information ◽  
The One

Based on the theory of peridynamics, the least squares and the moving least squares method are proposed to fit the physical information at nondiscrete points. It makes up for the shortcomings of the peridynamic method that only solves the discrete nodes and cannot obtain the physical information of other blank areas. The extended method is used to fit the one-way vibration problem of the rod, and the curve of the displacement of a nondiscrete node in the rod is extracted with time. The fitted displacement results are compared with the theoretical results to verify the feasibility of the fitting method. At the same time, the parameters in the fitting of the moving least squares method are optimized, and the effects of different tight weight functions and influence ranges on the results are analyzed. The results show that when the weight function is a power exponential function, the fitting effect increases with the decrease in the coefficient. When the weight function is a cubic spline weight function, a better fitting effect is obtained. And in the case of ensuring the fitting result, the affected area should be reduced as much as possible, and the calculation efficiency and precision can be improved.

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