11 papers
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…