arXiv subjects

Federico Lot

Publications and source records attributed to Federico Lot.

3 recordsLinked to original sources

arXiv2026

Adaptive RBF-multiscale approximation on bounded domains

This article addresses adaptivity in the kernel multiscale method. Adaptively compressed kernel multiscale approximations have already been presented and analyzed in (LeGia & Wendland, 2014). The main contribution of this work is to attempt to avoid using function evaluations which will be deleted in the compression step anyways. In order to work with function values, we always work in the Lagrange representation. We still assume to have all function values available to compute error norms, but we do not include those values in our approximations. Finally, we also employ local Lagrange function to further reduce the numerical work.

math.NA↗

arXiv2025

Efficiently parallelizable kernel-based multi-scale algorithm

The kernel-based multi-scale method has been proven to be a powerful approximation method for scattered data approximation problems which is computationally superior to conventional kernel-based interpolation techniques. The multi-scale method is based of an hierarchy of point clouds and compactly supported radial basis functions, typically Wendland functions. There is a rich body of literature concerning the analysis of this method including error estimates. This article addresses the efficient parallelizable implementation of those methods. To this end, we present and analyse a monolithic approach to compute the kernel-based multi-scale approximation.

math.NA↗

arXiv2022

Variably Scaled Persistence Kernels (VSPKs) for persistent homology applications

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 consider the idea of variably scaled kernels, for approximating functions and data, and we interpret it in the framework of persistent homology. We call them Variably Scaled Persistence Kernels (VSPKs). These new kernels are then tested in different classification experiments. The obtained results show that they can improve the performance and the efficiency of existing standard kernels.

math.NA↗