Singular Value Decomposition of the Radial Distribution Function for Hard Sphere and Square Well Potentials

We compute the singular value decomposition of the radial distribution function [Image: see text] for hard sphere, and square well solutions. We find that [Image: see text] decomposes into a small set of basis vectors allowing for an extremely accurate representation at all interpolated densities and potential strengths. In addition, we find that the coefficient vectors describing the magnitude of each basis vector are well described by a low-order polynomial. We provide a program to calculate [Image: see text] in this compact representation for the investigated parameter range.