A new formulation for total least square error method in d-dimensional space with mapping to a parametric line

2016 ◽  
Author(s):  
Vaclav Skala
Keyword(s):  
Dimensional Space ◽  
Least Square ◽  
Parametric Line ◽  
Total Least Square ◽  
New Formulation ◽  
Error Method

scholarly journals Improved Total Least Square Algorithm

2015 ◽  
Vol 9 (1) ◽  
pp. 394-399 ◽  
Author(s):  
Deng Yonghe
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Least Square ◽  
Error Equation ◽  
Virtual Observation ◽  
Straight Line ◽  
Condition Equation ◽  
Total Least Square ◽  
Three Dimensional Space ◽  
Improved Algorithm

Aim to blemish of total least square algorithm based on error equation of virtual observation,this paper proposed a sort of improved algorithm which doesn’t neglect condition equation of virtual observation,and considers both error equation and condition equation of virtual observation.So,the improved algorithm is better.Finally,this paper has fitted a straight line in three-dimensional space based on the improved algorithm.The result showed that the improved algorithm is viable and valid.

Why Is the Least Square Error Method Dangerous?

2021 ◽  
Vol 25 (1) ◽  
Author(s):  
Vaclav Skala ◽  
Edward Kansa
Keyword(s):  
Least Square ◽  
Error Method

scholarly journals A Sort of New Improved Algorithm For Total Least Square

2015 ◽  
Vol 9 (1) ◽  
pp. 238-247
Author(s):  
Deng Yonghe
Keyword(s):  
Least Square ◽  
New Method ◽  
Unknown Parameters ◽  
Error Equation ◽  
Virtual Observation ◽  
Condition Equation ◽  
Total Least Square ◽  
Improved Algorithm

Aim to blemish of total least square algorithm based on error equation of virtual observation, this paper put forward and deduced a sort of new improved algorithm which selects essential unknown parameters among designing matrix, and then, doesn’t consider condition equation of unknown parameters among designing matrix. So, this paper perfected and enriched algorithm, and sometimes, new method of this paper is better. Finally, the results of examples showed that new mothod is viable and valid.

Modified gradient algorithm for total least square filtering

2006 ◽  
Vol 70 (1-3) ◽  
pp. 568-576 ◽  
Author(s):  
Xiangyu Kong ◽  
Chongzhao Han ◽  
Ruixuan Wei
Keyword(s):  
Least Square ◽  
Gradient Algorithm ◽  
Total Least Square

Numerical treatment for solving two-dimensional space-fractional advection–dispersion equation using meshless method

2018 ◽  
Vol 32 (06) ◽  
pp. 1850073 ◽  
Author(s):  
Rongjun Cheng ◽  
Fengxin Sun ◽  
Qi Wei ◽  
Jufeng Wang
Keyword(s):  
Dispersion Equation ◽  
Convergence Rates ◽  
Dimensional Space ◽  
Energy Functional ◽  
Least Square ◽  
Approximation Schemes ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Moving Least Square ◽  
Advection Dispersion

Space-fractional advection–dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann–Liouville operator is discretized by the Grünwald formula. With center difference method, EFG method and Grünwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results by other well-known methods, the computed approximate solutions are presented in the format of tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error is computed and the proposed method has reasonable convergence rates in spatial and temporal discretizations.

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