Stable Computations with Gaussian Radial Basis Functions

By Bengt Fornberg, Elisabeth Larsson, Natasha Flyer. SIAM Journal on Scientific Computing, 2011

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Approximation of eigenfunctions in kernel-based spaces (2014, positive): “See [23] for a detailed discussion about this construction, and note that eigenfunction expansions play a central role in the RBF-QR technique dealt with in various papers [6, 8] recently.”
Solving PDEs with radial basis functions * (2015, methodology): “It was first implemented for nodes on the surface of a sphere [33], and more recently (in the special case of GA RBFs) for arbitrary node sets in 1-D, 2-D, and 3-D [29, 51].”
Robust rational interpolation and least-squares (2011, methodology): “For s uch problems an alternative known as the RBF-QR method is sometimes effec tive [8, 9].”
On the role of polynomials in RBF-FD approximations: I. Interpolation and accuracy (2016, methodology): “In double precision, using a stable algorithm such as RBF-QR [18, 25] or RBF-GA [20] gives full numerical access to small ε-values.”