MATLAB Implementation of Radial Basis Function

This article provides a MATLAB-implemented radial basis function code program. While maintaining simplicity and ease of use, we can further explore its underlying principles and applications. Radial basis functions serve as powerful tools for data interpolation and approximation problems. The fundamental principle involves mapping data points to a high-dimensional space, calculating distances between each data point and others, and utilizing a kernel function to determine interpolation or approximation weights. The code implementation demonstrates key aspects including: - Distance matrix computation using Euclidean norm - Kernel function selection (typically Gaussian, multiquadric, or inverse multiquadric) - Weight coefficient calculation through linear system solving - Interpolation surface generation using weighted summation This program showcases how radial basis functions can effectively solve interpolation challenges and can be readily adapted to custom datasets. Despite its straightforward implementation, the code provides excellent opportunities to deepen understanding of radial basis function applications and mathematical foundations through practical experimentation and modification. The implementation includes error handling and parameter tuning sections to ensure robust performance across different data characteristics.