2 citations · 4 across the 18 of their papers we have counts for
20 papers · 1 filter
Data-dependent Compact Multinode Shepard Method
Francesco Dell'Accio, Filomena Di Tommaso, Francesco Larosa +2
We introduce a data-dependent compact multinode Shepard method for the approximation of scattered multivariate data. The proposed approach extends the compact multinode Shepard ope…
Scattered data interpolation on the torus by compactly supported multinode Shepard operators
F. Dell'Accio, F. Di Tommaso, R. Lammirato +1
We introduce a compactly supported multinode Shepard operator for the interpolation of scattered data on the torus embedded in . The method combines local polynomial…
Polynomial interpolation--regression on the sphere
Francesco Dell'Accio, Federico Nudo, Teresa E. Pérez +1
We introduce an interpolation--regression operator for polynomial approximation on the unit sphere from discrete samples. The approximant is a spherical polynomial o…
A General Probability Density Framework for Local Histopolation and Weighted Function Reconstruction from Mesh Line Integrals
Francesco Dell'Accio, Allal Guessab, Mohammed Kbiri Alaoui +1
In this paper, we study the reconstruction of a bivariate function from weighted integrals along the edges of a triangular mesh, a problem of central importance in tomography, comp…
The univariate multinode Shepard method for the Caputo fractional derivatives: from Approximation to the solution of Bagley-Torvik equation
Francesco Dell'Accio, Filomena Di Tommaso, Ilde Ferrara
In this paper, we approximate the fractional derivative of a given function using the univariate multinode Shepard method through the Gauss-Jacobi quadrature formula. Subsequently,…
Multinode Shepard collocation method for pricing of financial derivatives
Francesco Dell'Accio, Filomena Di Tommaso, Elisa Francomano +1
This paper explores the use of the multinode Shepard method for the numerical solution of the two-dimensional Black-Scholes equation. The proposed approach integrates a spatial app…
Multinode Shepard Functions and Tensor Product Polynomial Interpolation: Applications to Digital Elevation Models
Domingo Barrera, Francesco Dell'Accio, Filomena Di Tommaso +5
The paper presents an in-depth exploration of the multinode Shepard interpolant on a regular rectangular grid, demonstrating its efficacy in reconstructing surfaces from DEM data.…
A rational quasi-interpolation operator for functions with jumps without the Gibbs phenomenon
Francesco Dell'Accio, Francesco Larosa, Federico Nudo +1
The study of quasi-interpolation has gained significant importance in numerical analysis and approximation theory due to its versatile applications in scientific and engineering fi…
Weighted and unweighted enrichment strategies for solving the Poisson problem with Dirichlet boundary conditions
Francesco Dell'Accio, Luca Desiderio, Allal Guessab +1
In this paper, we propose weighted and unweighted enrichment strategies to enhance the accuracy of the linear lagrangian finite element for solving the Poisson problem with Dirichl…
rational approximation and quasi-histopolation of functions with jumps through multinode Shepard functions
Francesco Dell'Accio, Francesco Larosa, Federico Nudo +1
Histopolation, or interpolation on segments, is a mathematical technique used to approximate a function over a given interval by exploiting integral information over…
A novel interpolation-regression approach for function approximation on the disk and its application to cubature formulas
Francesco Dell'Accio, Francisco Marcellán, Federico Nudo
The interpolation-regression approximation is a powerful tool in numerical analysis for reconstructing functions defined on square or triangular domains from their evaluations at a…
Nonconforming approximation methods for function reconstruction on general polygonal meshes via orthogonal polynomials
Francesco Dell'Accio, Allal Guessab, Gradimir V. Milovanović +1
In this work, we introduce new families of nonconforming approximation methods for reconstructing functions on general polygonal meshes. These methods are defined using degrees of…
Bivariate polynomial histopolation techniques on Padua, Fekete and Leja triangles
Ludovico Bruni Bruno, Francesco Dell'Accio, Wolfgang Erb +1
This paper explores the reconstruction of a real-valued function defined over a domain using bivariate polynomials that satisfy triangular histopolation…
Constrained mock-Chebyshev least squares approximation for Hermite interpolation
Francesco Dell'Accio, Francisco Marcellán, Federico Nudo
This paper addresses the challenge of function approximation using Hermite interpolation on equally spaced nodes. In this setting, standard polynomial interpolation suffers from th…
Polynomial histopolation on mock-Chebyshev segments
Ludovico Bruni Bruno, Francesco Dell'Accio, Wolfgang Erb +1
In computational practice, we often encounter situations where only measurements at equally spaced points are available. Using standard polynomial interpolation in such cases can l…
Nonsingularity of unsymmetric Kansa matrices: random collocation by MultiQuadrics and Inverse MultiQuadrics
R. Cavoretto, F. Dell'Accio, A. De Rossi +2
Unisolvence of unsymmetric Kansa collocation is still a substantially open problem. We prove that Kansa matrices with MultiQuadrics and Inverse MultiQuadrics for the Dirichlet prob…
Unisolvence of random Kansa collocation by Thin-Plate Splines for the Poisson equation
Francesco Dell'Accio, Alvise Sommariva, Marco Vianello
Existence of sufficient conditions for unisolvence of Kansa unsymmetric collocation for PDEs is still an open problem. In this paper we make a first step in this direction, proving…
A new quadratic and cubic polynomial enrichment of the Crouzeix-Raviart finite element
Francesco Dell'Accio, Allal Guessab, Federico Nudo
In this paper, we introduce quadratic and cubic polynomial enrichments of the classical Crouzeix--Raviart finite element, with the aim of constructing accurate approximations in su…
Numerical cubature on scattered data by adaptive interpolation
R. Cavoretto, F. Dell'Accio, A. De Rossi +4
We construct cubature methods on scattered data via resampling on the support of known algebraic cubature formulas, by different kinds of adaptive interpolation (polynomial, RBF, P…
Random sampling and unisolvent interpolation by almost everywhere analytic functions
Francesco Dell'Accio, Alvise Sommariva, Marco Vianello
We prove a.s. (almost sure) unisolvency of interpolation by continuous random sampling with respect to any given density, in spaces of multivariate a.e. (almost everywhere) analyti…