Error estimates for the interpolating moving least-squares method in n -dimensional space

Sun, Fengxin; Wang, Jufeng; Cheng, Yumin; Huang, Aixiang

doi:10.1016/j.apnum.2015.08.001

Cited by 63 publications

(16 citation statements)

References 76 publications

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“…In statistical and numerical analysis, Lagrange methods are used for polynomial interpolation. For a given number of points (xj, yj) , the Lagrange polynomial is the polynomial of lowest degree which supposes the value yj at each value xj , and it can be calculated using equations from ( 11) to ( 17) (Sun et al, 2015).…”

Section: B the Lagrange Interpolationmentioning

confidence: 99%

An Investigation on using Lagrange, Newton and Least Square Methods for Generating Nonlinear Interpolation Function for the Measuring Instruments

Mahmoud¹,

Gelany²

2021

ASMScJ

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This research is considered the milestone for metrologists to choose the appropriate method for determination of the nonlinear interpolation function for the measuring instruments. Three methods of generating the interpolation polynomial equations were investigated; Newton, Lagrange, and Least Square method. The response of the measuring instruments under investigation was calculated and compared with the experimental results. Least Square method was found that it is the most accurate and most realistic approach to determine the interpolation polynomial function for the measuring instruments. It is recommended to use Least Square method rather than other methods to interpolating the polynomial equation. This recommendation is very important for metrologist as well as for measuring instruments applicant. This article is millstone to determine the response of the measuring instrument at non calibrated points in the calibrated range.

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Section: B the Lagrange Interpolationmentioning

confidence: 99%

An Investigation on using Lagrange, Newton and Least Square Methods for Generating Nonlinear Interpolation Function for the Measuring Instruments

Mahmoud¹,

Gelany²

2021

ASMScJ

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“…移动最小二乘法(Moving Least-Squares Approximation, MLS)被广泛应用于无网格方法的形函数构造, 其泛函为加权最佳平方逼近形式, 因而有较高的计算精度; 程玉民等人 [10] 提出了改进的移动最小二乘法, 通过对基函数的正交化, 克服了移动最小二乘法易形成病态方程组的缺点. 为了解决无单元Galerkin方法等无网格方法不能直接施加本质边界条件的问题, Wang 等人 [11] 和Sun等人 [12] 建立了移动最小二乘插值法, 并研究了其误差分析理论. 为了解决无单元Galerkin方法等无网格方法计算量大的问题, Cheng等人 [13][14][15] [16] 建立了具有明确数学和物理意义的泛函, 提出了改进…”

Section: 王斌骅等中国科学: 物理学力学天文学 2017年第47卷第9期unclassified

The improved complex variable element-free Galerkin method for the analysis of Kirchhoff plates

Wang

Feng

et al. 2017

Sci. Sin.-Phys. Mech. Astron.

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“…Based on IMLS, the interpolating element-free Galerkin (IEFG) method [41] and other interpolation-type meshless methods [32,[42][43][44][45] were proposed. Wang et al studied the error convergence of the IMLS method [46,47]. The meshless method based on the IMLS method has a good calculation effect [48][49][50][51].…”

Section: Introductionmentioning

confidence: 99%

A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions

2021

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By introducing the dimension splitting method (DSM) into the improved interpolating moving least-squares (IMLS) method with nonsingular weight function, a dimension splitting–interpolating moving least squares (DS–IMLS) method is first proposed. Since the DSM can decompose the problem into a series of lower-dimensional problems, the DS–IMLS method can reduce the matrix dimension in calculating the shape function and reduce the computational complexity of the derivatives of the approximation function. The approximation function of the DS–IMLS method and its derivatives have high approximation accuracy. Then an improved interpolating element-free Galerkin (IEFG) method for the two-dimensional potential problems is established based on the DS–IMLS method. In the improved IEFG method, the DS–IMLS method and Galerkin weak form are used to obtain the discrete equations of the problem. Numerical examples show that the DS–IMLS and the improved IEFG methods have high accuracy.

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Error estimates for the interpolating moving least-squares method in n -dimensional space

Cited by 63 publications

References 76 publications

An Investigation on using Lagrange, Newton and Least Square Methods for Generating Nonlinear Interpolation Function for the Measuring Instruments

An Investigation on using Lagrange, Newton and Least Square Methods for Generating Nonlinear Interpolation Function for the Measuring Instruments

The improved complex variable element-free Galerkin method for the analysis of Kirchhoff plates

A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions

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