基于径向基函数的大数据曲面逼近方法比较研究
Big Geo Data Surface Approximation using Radial Basis Functions: A Comparative Study
摘要：
在许多工程问题中，散乱数据的近似处理是一项经常性的任务。径向基函数（RBF）近似适用于$n-$维空间中的大的分散数据集。它是一个不可分离的近似，因为它是基于两点之间的距离。这种方法导致一个超定线性方程组的解决方案。本文简要介绍了径向基函数（RBF）逼近方法，提出了一种新的大数据集的RBF逼近方法，并比较了不同的复杂支持的RBF（CS-RBF）的计算精度。所提出的方法利用矩阵的对称性，将矩阵划分为块和数据结构用于存储稀疏矩阵。对合成数据集和真实数据集进行了实验。
英文摘要：
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in $n-$dimensional space. It is a non-separable approximation, as it is based on the distance between two points. This method leads to the solution of an overdetermined linear system of equations. In this paper the RBF approximation methods are briefly described, a new approach to the RBF approximation of big datasets is presented, and a comparison for different Compactly Supported RBFs (CS-RBFs) is made with respect to the accuracy of the computation. The proposed approach uses symmetry of a matrix, partitioning the matrix into blocks and data structures for storage of the sparse matrix. The experiments are performed for synthetic and real datasets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
