scholarly journals A trimmed moving total least-squares method for curve and surface fitting

2020 ◽  
Vol 31 (4) ◽  
pp. 045003 ◽  
Author(s):  
Tianqi Gu ◽  
Yi Tu ◽  
Dawei Tang ◽  
Shuwen Lin ◽  
Bing Fang
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Surface Fitting ◽  
Total Least Squares ◽  
Curve And Surface Fitting

scholarly journals An Improved Moving Least Squares Method for Curve and Surface Fitting

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Lei Zhang ◽  
Tianqi Gu ◽  
Ji Zhao ◽  
Shijun Ji ◽  
Ming Hu ◽  
...  
Keyword(s):  
Least Squares ◽  
Random Error ◽  
Least Squares Method ◽  
Surface Fitting ◽  
Measured Data ◽  
Moving Least Squares ◽  
Generate Curve ◽  
Moving Least Squares Method ◽  
Curve And Surface Fitting ◽  
Mls Method

The moving least squares (MLS) method has been developed for the fitting of measured data contaminated with random error. The local approximants of MLS method only take the error of dependent variable into account, whereas the independent variable of measured data always contains random error. Considering the errors of all variables, this paper presents an improved moving least squares (IMLS) method to generate curve and surface for the measured data. In IMLS method, total least squares (TLS) with a parameterλbased on singular value decomposition is introduced to the local approximants. A procedure is developed to determine the parameterλ. Numerical examples for curve and surface fitting are given to prove the performance of IMLS method.

TOTAL LEAST SQUARES FOR ESTIMATION OF THE GROSS OUTPUT VECTOR

2020 ◽  
Author(s):  
Dmitriy Vladimirovich Ivanov ◽  
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Direct Costs ◽  
Total Least Squares ◽  
Test Cases ◽  
Output Vector ◽  
Final Consumption ◽  
The Matrix

The article proposes the estimation of the gross output vector in the presence of errors in the matrix of direct costs and the final consumption vector. The article suggests the use of the total least squares method for estimating the gross output vector. Test cases showed that the accuracy of the proposed estimates of the gross output vector is higher than the accuracy of the estimates obtained using the classical least squares method (OLS).

scholarly journals Array Pattern Synthesis Using a Hybrid Differential Evolution and Analytic Algorithm

Electronics ◽  
2021 ◽  
Vol 10 (18) ◽  
pp. 2227
Author(s):  
Rui Li ◽  
Le Xu ◽  
Xiaoqun Chen ◽  
Yong Yang ◽  
Xiaoning Yang ◽  
...  
Keyword(s):  
Differential Evolution ◽  
Least Squares ◽  
Antenna Array ◽  
Least Squares Method ◽  
Total Least Squares ◽  
Weight Matrix ◽  
Pattern Synthesis ◽  
Application Range ◽  
De Algorithm ◽  
Array Pattern

In this paper, a hybrid differential evolution and weight total least squares method (HDE-WTLSM) is proposed for antenna array pattern synthesis. A variable diagonal weight matrix is introduced in total least squares method. Then, the weight matrix is optimized by differential evolution (DE) algorithm to control the differences of the desired level and the obtained level in different directions. This algorithm combines the advantages of evolutionary algorithm and numerical algorithm, so it has a wider application range and faster convergence speed. To compare HDE-WTLSM with DE algorithm and typical numerical algorithms, these methods are applied to a linear antenna array and a conformal truncated conical array. Using our method, lower sidelobe levels and deeper nulls are obtained. The simulation results verify the validity and efficiently of HDE-WTLSM.

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