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Function approximation and interpolation play an essential role in most fields of computational sciences and engineering, such as data processing and numerical solution of partial differential equations (PDEs), in which the interpolation basis function is a key component. The traditional basis functions are mostly coordinate functions, such as polynomial and trigonometric functions, which are computationally expensive in dealing with high-dimensional problems due to their dependency on geometric complexity. Instead, radial basis functions (RBFs) are constructed in terms of a one-dimension distance variable, irrespective of dimensionality of problems, and appear to have a clear edge over the traditional polynomial basis functions.

RBFs were originally introduced in the early 1970s to multivariate scattered data approximations and function interpolations. Now, it is broadly employed in the neural network and …