A Simplified Interpolating Moving Least-Squares Method and its Error Estimates

2011 ◽  
Vol 101-102 ◽  
pp. 271-274
Author(s):  
Ju Feng Wang
Keyword(s):  
Error Estimate ◽  
Least Squares ◽  
Shape Function ◽  
Least Squares Method ◽  
Delta Function ◽  
Moving Least Squares ◽  
Approximation Function ◽  
Kronecker Delta ◽  
Moving Least Squares Method ◽  
Mls Approximation

A disadvantage of the MLS approximation is that the shape function of this method does not satisfy the property of Kronecker Delta function. Thus developing an interpolating MLS approximation is very important. In this paper, the interpolating moving least-squares (IMLS) method presented by Lancaster and Salkauskas is discussed in detail and a simplified expression of the approximation function of the IMLS method is given. The simpler expression makes it more convenient to use this method. The error estimate of the approximation function also is discussed. And a numerical example is given to confirm the results.

scholarly journals Multi-Dimensional Moving Least Squares Method for Elasticity Problems

2012 ◽  
Vol 78 (786) ◽  
pp. 142-151
Author(s):  
Kohei SAKIHARA ◽  
Hitoshi MATSUBARA ◽  
Takaaki EDO ◽  
Hisao HARA ◽  
Genki YAGAWA
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Moving Least Squares ◽  
Moving Least Squares Method ◽  
Elasticity Problems

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.

RESPONSE SURFACE MODEL USING MOVING LEAST SQUARES METHOD

2000 ◽  
Vol 2000.4 (0) ◽  
pp. 181-186
Author(s):  
Akihiro KAMINAGA ◽  
Katsuyuki SUZUKI ◽  
Daiji FUJII ◽  
Hideomi OHTSUBO
Keyword(s):  
Least Squares ◽  
Response Surface ◽  
Least Squares Method ◽  
Response Surface Model ◽  
Moving Least Squares ◽  
Surface Model ◽  
Moving Least Squares Method

Integration of Moving Least Squares Method and Multilevel B-Spline Method for Scattered Data Approximation

2011 ◽  
Vol 291-294 ◽  
pp. 2245-2249
Author(s):  
Shi Ju Yan ◽  
Bin Ge
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Scattered Data ◽  
Moving Least Squares ◽  
Scattered Data Approximation ◽  
Approximation Accuracy ◽  
Data Approximation ◽  
B Spline ◽  
Moving Least Squares Method ◽  
Method Accuracy

For scattered data approximation with multilevel B-spline(MBS) method, accuracy could be enhanced by densifying control lattice. Nevertheless, when control lattice density reaches to some extent, approximation accuracy could not be enhanced further. A strategy based on integration of moving least squares(MLS) and multilevel B-spline(MBS) is presented. Experimental results demonstrate that the presented strategy has higher approximation accuracy.

THE INTERPOLATING ELEMENT-FREE GALERKIN (IEFG) METHOD FOR TWO-DIMENSIONAL ELASTICITY PROBLEMS

2011 ◽  
Vol 03 (04) ◽  
pp. 735-758 ◽  
Author(s):  
HONGPING REN ◽  
YUMIN CHENG
Keyword(s):  
Least Squares ◽  
Shape Function ◽  
Weak Form ◽  
New Method ◽  
Moving Least Squares ◽  
Two Dimensional ◽  
Element Free Galerkin ◽  
Elasticity Problems ◽  
Mls Approximation ◽  
Element Free

In this paper, a new method for deriving the moving least-squares (MLS) approximation is presented, and the interpolating moving least-squares (IMLS) method proposed by Lancaster is improved. Compared with the IMLS method proposed by Lancaster, a simpler formula of the shape function is given in the improved IMLS method in this paper so that the new method has higher computing efficiency. Combining the shape function constructed by the improved IMLS method with Galerkin weak form of the elasticity problems, the interpolating element-free Galerkin (IEFG) method for the two-dimensional elasticity problems is presented, and the corresponding formulae are obtained. In the IEFG method, the boundary conditions can be applied directly which makes the computing efficiency higher than the conventional EFG method. Some numerical examples are presented to demonstrate the validity of the method.

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