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Abstract
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Due to the high approximation power and simplicity of computation of smooth radial basis
functions (RBFs), in recent decades they have received much attention for function approximation. These
RBFs contain a shape parameter that regulates their approximation power and stability but its optimal
selection is challenging. To avoid this difficulty, this paper follows a novel and computationally efficient
strategy to propose a space of radial polynomials with even degree that well approximates flat RBFs. The
proposed space, Hn, is the shifted radial polynomials of degree 2n. By obtaining the dimension of Hn
and introducing a basis set, it is shown that Hn is considerably smaller than P2n while the distances from
RBFs to both Hn and P2n are nearly equal. For computation, by introducing new basis functions, two
computationally efficient approaches are proposed. Finally, the presented theoretical studies are verified
by the numerical results.
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