arXiv subjects

Salah Eddargani

Publications and source records attributed to Salah Eddargani.

4 recordsLinked to original sources

arXiv2025

Multinode Shepard Functions and Tensor Product Polynomial Interpolation: Applications to Digital Elevation Models

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. Additionally, we study the approximation order associated to this interpolant and present a detailed algorithm for reconstructing surfaces. Numerical tests showcase the effectiveness of the proposed algorithm.

math.NA↗

arXiv2024

Quadrature rules for splines of high smoothness on uniformly refined triangles

In this paper, we identify families of quadrature rules that are exact for sufficiently smooth spline spaces on uniformly refined triangles in $\mathbb{R}^2$. Given any symmetric quadrature rule on a triangle $T$ that is exact for polynomials of a specific degree $d$, we investigate if it remains exact for sufficiently smooth splines of the same degree $d$ defined on the Clough-Tocher 3-split or the (uniform) Powell-Sabin 6-split of $T$. We show that this is always true for $C^{2r-1}$ splines having degree $d=3r$ on the former split or $d=2r$ on the latter split, for any positive integer $r$. Our analysis is based on the representation of the considered spline spaces in terms of suitable simplex splines.

math.NA↗

arXiv2024

Minimal time of the pointwise controllability for degenerate singular operators and related numerical results via B-splines

The goal of this paper is to analyze the pointwise controllability properties of a one-dimensional degenerate/singular equation. We prove the conditions that characterize approximate and null controllability. Besides, a numerical simulation based on B-splines will be provided, in which the state $u$ and the control function $h$ are represented in terms of B-spline basis functions. The numerical results obtained match the theoretical ones.

math.OC↗

arXiv2024

Construction of 2D explicit cubic quasi-interpolating splines in Bernstein-Bézier form

In this paper, the construction of $C^{1}$ cubic quasi-interpolants on a three-direction mesh of $\RR^{2}$ is addressed. The quasi-interpolating splines are defined by directly setting their Bernstein-Bézier coefficients relative to each triangle from point and gradient values in order to reproduce the polynomials of the highest possible degree. Moreover, additional global properties are required. Finally, we provide some numerical tests confirming the approximation properties.

math.NA↗