A Radial Basis Function Approximation for Large Datasets

TL;DR

This paper introduces a new RBF approximation method for large datasets that leverages matrix symmetry and partitioning to improve computational accuracy in engineering applications.

Contribution

A novel RBF approximation approach for large datasets utilizing matrix symmetry and block partitioning, enhancing accuracy and efficiency.

Findings

Effective approximation of large scattered datasets demonstrated

Improved accuracy with different RBFs and datasets

Experimental results validate the proposed method

Abstract

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered datasets in d-dimensional space. It is non-separable approximation, as it is based on a distance between two points. This method leads to a solution of overdetermined linear system of equations. In this paper a new approach to the RBF approximation of large datasets is introduced and experimental results for different real datasets and different RBFs are presented with respect to the accuracy of computation. The proposed approach uses symmetry of matrix and partitioning matrix into blocks.