Jumping with variably scaled discontinuous kernels (VSDKs)

DOI10.1007/s10543-019-00786-zOpenAlexW2991483536WikidataQ126783459 ScholiaQ126783459MaRDI QIDQ2185872

Emma Perracchione, F. Marchetti, Stefano De Marchi

Publication date: 5 June 2020

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-019-00786-z

zbMATH Keywords

Gibbs phenomenonmeshfree methodsdiscontinuous kernelsRBF approximationscattered data interpolationapplications to satellite images

Mathematics Subject Classification ID

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

Related Items (15)

A greedy non-intrusive reduced order model for shallow water equations ⋮ Multivariate approximation at fake nodes ⋮ Shape-Driven Interpolation With Discontinuous Kernels: Error Analysis, Edge Extraction, and Applications in Magnetic Particle Imaging ⋮ A regularization-correction approach for adapting subdivision schemes to the presence of discontinuities ⋮ Data-Driven Kernel Designs for Optimized Greedy Schemes: A Machine Learning Perspective ⋮ Moving least squares approximation using variably scaled discontinuous weight function ⋮ A modified kernel-based collocation method for interface boundary value problems ⋮ Numerical simulation of a prostate tumor growth model by the RBF-FD scheme and a semi-implicit time discretization ⋮ The extension of Rippa's algorithm beyond LOOCV ⋮ On the reconstruction of discontinuous functions using multiquadric RBF-WENO local interpolation techniques ⋮ Polynomial interpolation via mapped bases without resampling ⋮ Data-driven extrapolation via feature augmentation based on variably scaled thin plate splines ⋮ Feature augmentation for the inversion of the Fourier transform with limited data ⋮ Learning via variably scaled kernels ⋮ Mapped polynomials and discontinuous kernels for Runge and Gibbs phenomena

Uses Software

• Matlab
• GaussQR
• rbf_qr
• FakeNodes

Cites Work

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• Near-optimal data-independent point locations for radial basis function interpolation
• Polynomial interpolation via mapped bases without resampling
• Partition of unity interpolation using stable kernel-based techniques
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• Stable Computations with Gaussian Radial Basis Functions
• On the Gibbs Phenomenon and Its Resolution
• Shape-Driven Interpolation With Discontinuous Kernels: Error Analysis, Edge Extraction, and Applications in Magnetic Particle Imaging
• Interpolation with variably scaled kernels
• Caratheodory-Tchakaloff Subsampling
• A Trivariate Interpolation Algorithm Using a Cube-Partition Searching Procedure
• Scattered Data Approximation

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