Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations

By Edward J. Kansa, Yiu Chung Benny Hon, Hong Kong, H. Kowloon, Kong. 2000

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Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier–Stokes equations (2003, methodology): “To remove this difficulty, Kansa [20] recommended the replacement of global solvers by block partitioning and LU decomposition schemes for large simulation problems.”
The Runge phenomenon and spatially variable shape parameters in RBF interpolation (2007, methodology): “by the Contour–Padé algorithm or by the RBF-QR algorithm; certain pre-conditioning-type methods [15,16] can alleviate but will not eliminate ill-conditioning).”
A random variable shape parameter strategy for radial basis function approximation methods (2009, background): “However Scientists and Engineers have shown in numerous works, including [2, 3, 8, 9, 5, 6, 7], that in terms of the accuracy of RBF methods that variable shape parameter strategies may have an advantage over a constant shape parameter strategy.”
Scattered node compact finite difference-type formulas generated from radial basis functions (2006, background): “Some attempts have been made to resolve this problem [3,5,6] (and the references therein).”