An acceleration method for moving least squares based on a generalized octree for massive data

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-07-03 DOI:10.1016/j.cam.2025.116893

Sanpeng Zheng

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引用次数: 0

Abstract

Moving least squares (MLS) method is one of the most classical methods in scattered data fitting. To improve computational efficiency and approximation accuracy, the compact support weight functions are used. However, due to “moving” in MLS, the approximations at different points are obtained by solving different weighted least squares problems, which significantly reduces the computational efficiency of MLS for massive data, especially in problems that require multiple approximations. To improve the computational efficiency, this paper proposes an acceleration method based on a generalized octree. This method reduces the time of the neighborhood search in MLS based on the specific data structure, improves the computational efficiency and preserves the approximation results of MLS. Numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed method in comparison with the acceleration methods based on kd-tree and piecewise computation under data sets with various sizes and dimensions.

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基于广义八叉树的海量数据移动最小二乘加速方法

移动最小二乘法（MLS）是离散数据拟合中最经典的方法之一。为了提高计算效率和逼近精度，采用了紧凑的支持权函数。然而，由于MLS中的“移动”，不同点的近似是通过求解不同的加权最小二乘问题来获得的，这大大降低了MLS对于海量数据的计算效率，特别是在需要多次近似的问题中。为了提高计算效率，本文提出了一种基于广义八叉树的加速方法。该方法根据特定的数据结构，减少了MLS中邻域搜索的时间，提高了计算效率，并保留了MLS的近似结果。在不同尺寸和维度的数据集上，与基于kd树和分段计算的加速方法进行了比较，验证了该方法的有效性和准确性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.