Federico Nudo

Conditioning and Singular Value Distribution of Jacobi Weighted Histopolation Matrices

Allal Guessab, Federico Nudo, Stefano Serra-Capizzano

In this paper, we first study the singular value distribution of the unscaled matrices arising from Jacobi weighted histopolation. For the Jacobi weight with parameters $(α, β)$ , an…

Exactly Diagonal Gram Matrices in Jacobi Weighted Histopolation

Allal Guessab, Federico Nudo, Stefano Serra-Capizzano

In the current work, we study univariate polynomial weighted histopolation on $[- 1, 1]$ , where the data are weighted integrals over a family of intervals. After choosing a polynomia…

Weighted Derivative Histopolation on Arbitrary Grids: Admissibility and Exact Factorizations

Allal Guessab, Federico Nudo

In this paper, we introduce a weighted derivative histopolation framework on families of intervals. The degrees of freedom consist of one scalar normalization and weighted integral…

Spectral distribution of Jacobi weighted histopolation matrices via GLT theory

Allal Guessab, Federico Nudo, Stefano Serra-Capizzano

In this paper we study a weighted histopolation problem on $[- 1, 1]$ associated with Jacobi weights. In the first part of the present work we prove results in approximation theory,…

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 $S^{2}$ from discrete samples. The approximant is a spherical polynomial o…

Spectral Schur analysis of structured moment matrices for quadratic histopolation

Allal Guessab, Federico Nudo

In this paper we study parameter-dependent structured moment matrices with a canonical block form arising from weighted quadratic histopolation on simplicial meshes. For a strictly…

Generalized Probability Density Approach to Histopolation Schemes of Arbitrary Order

Gradimir V. Milovanovic, Federico Nudo

In this paper, we investigate the reconstruction of a bivariate function from weighted edge integrals on a triangular mesh, a problem of central importance in tomography, computer…

Quadratic Weighted Histopolation on Tetrahedral Meshes with Probabilistic Degrees of Freedom

Allal Guessab, Federico Nudo

In this paper we introduce three complementary three-dimensional weighted quadratic enrichment strategies to improve the accuracy of local histopolation on tetrahedral meshes. The…

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…

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 $C^{\infty}$ 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…

$C^{\infty}$ 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 $f$ over a given interval $I = [a, b]$ 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 $f$ defined over a domain $Ω \subset R^{2}$ 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…

Two one-parameter families of nonconforming enrichments of the Crouzeix-Raviart finite element

Federico Nudo

In this paper, we introduce two one-parameter families of quadratic polynomial enrichments designed to enhance the accuracy of the classical Crouzeix--Raviart finite element. These…

A general quadratic enrichment of the Crouzeix--Raviart finite element

Federico Nudo

The Crouzeix--Raviart finite element method is widely recognized in the field of finite element analysis due to its nonconforming nature. The main goal of this paper is to present…