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- W2992921446 abstract "Gaussian kernels can be an efficient and accurate tool for multivariate interpolation. For smooth functions, high accuracies are often achieved near the flat limit where the interpolation matrix becomes increasingly ill-conditioned. Stable evaluation algorithms for isotropic Gaussians (Gaussian radial basis functions) have been proposed based on a Chebyshev expansion of the Gaussians by Fornberg, Larsson, and Flyer and based on a Mercer expansion with Hermite polynomials by Fasshauer and McCourt. In this paper, we propose a new stabilization algorithm for the multivariate interpolation with isotropic or anisotropic Gaussians for an arbitrary number of dimensions derived from the generating function of the Hermite polynomials. We also derive and analyze a new analytic cutoff criterion for the generating function expansion that allows us to automatically adjust the number of stabilizing basis functions." @default.
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- W2992921446 date "2019-01-01" @default.
- W2992921446 modified "2023-09-27" @default.
- W2992921446 title "Stable Interpolation with Isotropic and Anisotropic Gaussians Using Hermite Generating Function" @default.
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- W2992921446 doi "https://doi.org/10.1137/19m1262449" @default.
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