On spline quasi-interpolation through dimensions

Dagnino, Catterina; Lamberti, Paola; Remogna, Sara

doi:10.1007/s11565-022-00427-4

Cited by 4 publications

(1 citation statement)

References 77 publications

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“…The interpolant also retains the property of exponential decay at infinity of the Gaussian kernel. As quasi-interpolation provides direct solutions without any need to solve large algebraic systems of equations [11], when compared to other mesh-free techniques such as RBF interpolation, this approach can approximate the function in less computational time in higher dimensions. Quasi-interpolation has been successfully applied to scattered data approximation and interpolation, numerical solutions to partial differential equations, and quadrature.…”

Section: Introductionmentioning

confidence: 99%

Quasi-Interpolation on Chebyshev Grids with Boundary Corrections

Alsharif

2024

Computation

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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. This study introduces a novel approach to quasi-interpolation modification, which significantly enhances convergence rates and minimizes errors at boundary points, thereby advancing the methods for boundary approximation.

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Section: Introductionmentioning

confidence: 99%