RBF-GA Differentiation Weights

Compute differentiation weights from nearly flat radial basis functions using the RBF-GA algorithm.

Radial basis functions (RBFs) provide an alternative to polynomials for computing finite difference weights on scattered nodes. In the limit as the basis functions become flat, Gaussian RBFs reproduce the polynomial weights, and can thus be viewed as a generalization of classical finite differences. However, nearly flat basis functions are unsuitable for computations, since the basis matrix is ill-conditioned. The RBF-GA algorithm circumvents this problem by constructing a well-conditioned basis for the same space.
For more information, see
Fornberg, Bengt, Erik Lehto, and Collin Powell. "Stable calculation of Gaussian-based RBF-FD stencils." Computers & Mathematics with Applications 65.4 (2013): 627-637.