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Sobolev Algorithm for Local Smoothness Analysis (SALSA) via Sharp Direct and Inverse Statements
Sara Avesani, Leevan Ling, Francesco Marchetti +1
We extend sharp direct and inverse approximation statements for kernel-based methods for finitely smooth kernels, i.e. those whose native spaces are norm-equivalent to Sobolev spac…
A fast surrogate cross validation algorithm for meshfree RBF collocation approaches
Francesco Marchetti
Cross validation is an important tool in the RBF collocation setting, especially for the crucial tuning of the shape parameter related to the radial basis function. In this paper,…
Mapped Variably Scaled Kernels: Applications to Solar Imaging
Francesco Marchetti, Emma Perracchione, Anna Volpara +3
Variably scaled kernels and mapped bases constructed via the so-called fake nodes approach are two different strategies to provide adaptive bases for function interpolation. In thi…
Polynomial mapped bases: theory and applications
Stefano De Marchi, Giacomo Elefante, Elisa Francomano +1
In this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-…
Variably Scaled Persistence Kernels (VSPKs) for persistent homology applications
Stefano De Marchi, Federico Lot, Francesco Marchetti +1
In recent years, various kernels have been proposed in the context of persistent homology to deal with persistence diagrams in supervised learning approaches. In this paper, we con…
Efficient Reduced Basis Algorithm (ERBA) for kernel-based approximation
Francesco Marchetti, Emma Perracchione
The main purpose of this work is the one of providing an efficient scheme for constructing reduced interpolation models for kernel bases. In literature such problem is mainly addre…