82 citations · 157 across the 22 of their papers we have counts for
23 papers
Generalized MLS and LS-SVR for Allen-Cahn Equations on Spheres
Vahid Mohammadi, Mehdi Dehghan, Stefano De Marchi
This work extends least-squares support vector regression (LS-SVR) based on the generalized moving least squares (GMLS) approximation to the numerical solution of partial different…
Mapping for Approximation: A Unified View of Rescaled, Variably Scaled and Rational Kernel Methods
Stefano De Marchi
Classical approximation methods are usually improved by changing the sampling set, increasing the number of data points, or selecting a different basis. We advocate a complementary…
Results, challenges and new steps on RBF approximation and computation
Stefano De Marchi, Nadaniela Egidi, Josephin Giacomini +1
We present an up-to-date overview of approximation methods based on Radial Basis Function (RBF) techniques, which have recently attracted attention across various computational too…
Geometric properties of the Lebesgue function
Leokadia Białas-Cież, Stefano De Marchi, Mateusz Suder
We present a collection of observations concerning the peculiar behavior of the Lebesgue function in the setting of the interval and the square $[-1,1]^2…
Persistence kernels for classification: A comparative study
Cinzia Bandiziol, Stefano De Marchi
The aim of the present work is a comparative study of different persistence kernels applied to various classification problems. After some necessary preliminaries on homology and p…
-convergence of Kantorovich-type Max-Min Neural Network Operators
İsmail Aslan, Stefano De Marchi, Wolfgang Erb
In this work, we study the Kantorovich variant of max-min neural network operators, in which the operator kernel is defined in terms of sigmoidal functions. Our main aim is to demo…
More properties of -Chebyshev functions and points
Stefano De Marchi, Giacomo Elefante, Francesco Marchetti +1
Recently, -Chebyshev functions, as well as the corresponding zeros, have been introduced as a generalization of classical Chebyshev polynomials of the first kind and related…
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…
Moving Least Squares Approximation using Variably Scaled Discontinuous Weight Function
Mohammad Karimnejad Esfahani, Stefano De Marchi, Francesco Marchetti
Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications a…
Greedy algorithms for learning via exponential-polynomial splines
Rosanna Campagna, Stefano De Marchi, Emma Perracchione +1
Kernel-based schemes are state-of-the-art techniques for learning by data. In this work we extend some ideas about kernel-based greedy algorithms to exponential-polynomial splines,…
Stable discontinuous mapped bases: the Gibbs-Runge-Avoiding Stable Polynomial Approximation (GRASPA) method
Stefano De Marchi, Giacomo Elefante, Francesco Marchetti
The mapped bases or Fake Nodes Approach (FNA), introduced in [10], allows to change the set of nodes without the need of resampling the function. Such scheme has been successfully…
On -Chebyshev functions and points of the interval
Stefano De Marchi, Giacomo Elefante, Francesco Marchetti
In this paper, we introduce the class of -Chebyshev functions and corresponding points, which can be seen as a family of {\it generalized} Chebyshev polynomials and points.…
Shape-Driven Interpolation with Discontinuous Kernels: Error Analysis, Edge Extraction and Applications in MPI
Stefano De Marchi, Wolfgang Erb, Francesco Marchetti +2
Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study…
A rescaled method for RBF approximation
Stefano De Marchi, Andrea Idda, Gabriele Santin
In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel inter…
Partition of unity interpolation using stable kernel-based techniques
R. Cavoretto, S. De Marchi, A. De Rossi +2
In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) met…
Approximating basins of attraction for dynamical systems via stable radial bases
Roberto Cavoretto, Stefano De Marchi, Alessandra De Rossi +2
In applied sciences, such as physics and biology, it is often required to model the evolution of populations via dynamical systems. In this paper, we focus on the problem of approx…
Trivariate polynomial approximation on Lissajous curves
Len Bos, Stefano De Marchi, Marco Vianello
We study Lissajous curves in the 3-cube, that generate algebraic cubature formulas on a special family of rank-1 Chebyshev lattices. These formulas are used to construct trivariate…
On the constrained mock-Chebyshev least-squares
Stefano De Marchi, Francesco Dell'Accio, Mariarosa Mazza
The algebraic polynomial interpolation on uniformly distributed nodes is affected by the Runge phenomenon, also when the function to be interpolated is analytic. Among all techniqu…
On certain multivariate Vandermonde determinants whose variables separate
Stefano De Marchi, Konstantin Usevich
We prove that for almost square tensor product grids and certain sets of bivariate polynomials the Vandermonde determinant can be factored into a product of univariate Vandermonde…
A new stable basis for RBF approximation
Gabriele Santin
It's well know that Radial Basis Function approximants suffers of bad conditioning if the simple basis of translates is used. A recent work of M.Pazouki and R.Schaback gives a quit…
Polynomial approximation and cubature at approximate Fekete and Leja points of the cylinder
Stefano De Marchi
The paper deals with polynomial interpolation, least-square approximation and cubature of functions defined on the rectangular cylinder, , with the unit disk.…
New cubature formulae and hyperinterpolation in three variables
Stefano De Marchi, Marco Vianello, Yuan Xu
A new algebraic cubature formula of degree for the product Chebyshev measure in the -cube with nodes is established. The new formula is then applied…
Bivariate Lagrange interpolation at the Padua points: the ideal theory approach
Len Bos, Stefano De Marchi, Marco Vianello +1
Padua points is a family of points on the square given by explicit formulas that admits unique Lagrange interpolation by bivariate polynomials. The interpolation polynom…