An examination of evaluation algorithms for the RBF method

Radial Basis Function (RBF) methods are important tools for scattered data interpolation and for the solution of PDEs in complexly shaped domains. Several approaches for the evaluation of RBF methods are known. To date, the most noteworthy methods are solving a linear system in the standard RBF basis using both double and extended precision floating point arithmetic and two approaches that make a change of basis for the purpose of obtaining a better conditioned linear system. In this work the approaches are compared and contrasted for the purpose of illustrating the strengths and weakness of each method as well as to give insight into the application of each approach.