Data dependent weights in discontinuous weighted least-squares approximation with anisotropic support
Data dependent weights in discontinuous weighted least-squares approximation with anisotropic support
复制标题
具有各向异性支持的不连续加权最小二乘近似中的数据相关权重
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
N. Petrovskaya
中科院分区：
文献类型：
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作者：
N. Petrovskaya
不连续加权最小二乘 (DWLS) 近似是加权最小二乘方法的修改，需要局部支持（重建模板）来逼近给定点处的函数。 DWLS 方法通常用于在不规则计算网格上近似函数的计算问题。最近发现，该方法在不规则网格上提供了不准确的近似，并且对不规则粗网格上的重建模板捕获的远处点的传统加权并不能提高近似的准确性。因此，在我们的论文中，我们进一步研究了远距离点对 DWLS 近似精度的影响，并为 DWLS 重建设计了新的权重系数，以获得更准确的重建结果。我们的方法基于作者之前作品中最初开发的数值距离点的概念，作为新的权重函数计算数据空间中两点之间的距离。
Discontinuous weighted least-squares (DWLS) approximation is modification of a weighted least-squares method that requires a local support (a reconstruction stencil) to approximate a function at a given point. A DWLS method is often employed in computational problems where a function is approximated on an irregular computational grid. It has recently been revealed that the method provides inaccurate approximation on irregular grids and conventional weighting of distant points captured by a reconstruction stencil on an irregular coarse mesh does not improve the accuracy of the approximation. Thus in our paper we further investigate the impact of distant points on the accuracy of DWLS approximation and design new weight coefficients for DWLS reconstruction that allow one to obtain more accurate reconstruction results. Our approach is based on a concept of numerically distant points originally developed in author’s previous works, as a new weight function calculates the distance between two points in the data space.