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Radial polynomials as alternatives to flat radial basis functions | ||
| Journal of Mathematical Modeling | ||
| مقاله 10، دوره 12، شماره 2، مهر 2024، صفحه 337-354 اصل مقاله (541.32 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2024.26001.2304 | ||
| نویسندگان | ||
| Fatemeh Pooladi؛ hosseinzadeh Hosseinzadeh* | ||
| Department of Mathematics, Persian Gulf University, Bushehr, Iran | ||
| چکیده | ||
| 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, $\mathcal{H}_n$, is the shifted radial polynomials of degree $2n$. By obtaining the dimension of $\mathcal{H}_n$ and introducing a basis set, it is shown that $\mathcal{H}_n$ is considerably smaller than $\mathcal{P}_{2n}$ while the distances from RBFs to both $\mathcal{H}_n$ and $\mathcal{P}_{2n}$ 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. | ||
| کلیدواژهها | ||
| Smooth radial basis function؛ radial polynomial؛ Numerical approximation؛ Interpolation | ||
| مراجع | ||
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