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Quasi-Interpolation on Chebyshev Grids with Boundary Corrections
Version 1
: Received: 25 April 2024 / Approved: 26 April 2024 / Online: 26 April 2024 (11:52:07 CEST)
A peer-reviewed article of this Preprint also exists.
Alsharif, F. Quasi-Interpolation on Chebyshev Grids with Boundary Corrections. Computation 2024, 12, 100. Alsharif, F. Quasi-Interpolation on Chebyshev Grids with Boundary Corrections. Computation 2024, 12, 100.
Abstract
Quasi-interpolation is a powerful tool for approximating functions using radial basis functions (RBFs) such as Gaussian kernels. This avoids solving large systems of equations as in RBF interpolation. However, quasi-interpolation with Gaussian kernels on compact intervals can have significant errors near the boundaries. This paper proposes a quasi-interpolation method with Gaussian kernels using Chebyshev points and boundary corrections to improve the approximation near the boundaries. The boundary corrections use a linear approximation of the function beyond the interval to estimate the truncation error and add correction terms. Numerical studies on test functions show that the proposed method reduces errors significantly near boundaries compared to quasi-interpolation without corrections, for both equally spaced and Chebyshev points. The convergence and accuracy with the boundary corrections are generally better with Chebyshev points compared to equally spaced points. The proposed method provides an efficient way to perform quasi-interpolation on compact intervals while controlling the boundary errors.
Keywords
Quasi-Interpolation; Radial basis functions; Boundary corrections; Chebyshev Points; Univariate Interpolation
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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