Analytical formulas for polynomial coefficients in radial basis function interpolation

Radial basis functions (RBF) are used in many areas, including interpolation and approximation, solution of partial differential equations, neural networks, and machine learning. RBFs are based on the sum of weighted kernel functions. Additional orthogonal polynomials are added for robustness, numerical stability, and computational efficiency improvement.This contribution gives a new analytical formula specifying values of the polynomial coefficients used in RBF interpolation. The zerodegree pol