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A Convex Combined Density Function Used in Gaussian Radial Basis Function Interpolation.

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Bibliographic Details
Title: A Convex Combined Density Function Used in Gaussian Radial Basis Function Interpolation.
Authors: Chen, Zhanheng1 (AUTHOR), Ailaiti, Bupatiman1 (AUTHOR), Yuan, Daming1,2,3 (AUTHOR) dmyuan@jxnu.edu.cn, Chen, Yanliang2 (AUTHOR)
Source: Mathematical Methods in the Applied Sciences. 11/30/2025, Vol. 48 Issue 17, p15904-15913. 10p.
Subject Terms: *INTERPOLATION, *MATHEMATICAL optimization, *RADIAL basis functions, *PROBABILITY density function, *PARAMETERIZATION, *EMPIRICAL research, *MACHINE learning
Abstract: For Gaussian radial basis function (GRBF) interpolation with a fixed number of interpolation points, a lower shape parameter is more appropriate for Chebyshev points, though this can lead to a singular system. In contrast, a higher parameter suits evenly spaced points but may reduce interpolation accuracy. This study introduces a combined density function, a convex combination of the Chebyshev measure and the limiting measure of equally spaced grids. Optimal combined coefficients and distributed points are determined by solving an unconstrained optimization problem using machine learning. Numerical tests show that a more moderate shape parameter can be used with the combined density function, effectively balancing singularity and accuracy. [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
Description
Abstract:For Gaussian radial basis function (GRBF) interpolation with a fixed number of interpolation points, a lower shape parameter is more appropriate for Chebyshev points, though this can lead to a singular system. In contrast, a higher parameter suits evenly spaced points but may reduce interpolation accuracy. This study introduces a combined density function, a convex combination of the Chebyshev measure and the limiting measure of equally spaced grids. Optimal combined coefficients and distributed points are determined by solving an unconstrained optimization problem using machine learning. Numerical tests show that a more moderate shape parameter can be used with the combined density function, effectively balancing singularity and accuracy. [ABSTRACT FROM AUTHOR]
ISSN:01704214
DOI:10.1002/mma.70059