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Jumping with variably scaled discontinuous kernels (VSDKs). (English) Zbl 07209368

Summary: In this paper we address the problem of approximating functions with discontinuities via kernel-based methods. The main result is the construction of discontinuous kernel-based basis functions. The linear spaces spanned by these discontinuous kernels lead to a very flexible tool which sensibly or completely reduces the well-known Gibbs phenomenon in reconstructing functions with jumps. For the new basis we provide error bounds and numerical results that support our claims. The method is also effectively tested for approximating satellite images.

MSC:

65D05 Numerical interpolation
65D15 Algorithms for approximation of functions
41A05 Interpolation in approximation theory
41A25 Rate of convergence, degree of approximation
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