A Shepard-like Hermite interpolation operator with fourth approximation order Barrera Rosillo, Domingo Nouisser, Otheman Zerroudi, Benaissa Scattered data interpolation Interpolation algorithms Shepard method From a first order Hermite interpolant on a triangle written in terms of barycentric coordinates, a Shepard-like interpolation is defined. It achieves fourth order of approximation. Its performance is checked by considering well-known test functions as well different Delaunay triangulations. The novel operator is compared to a Shepard-type operator and to a Hermite cubic interpolant over a Powell–Sabin partition. 2025-11-04T09:29:49Z 2025-11-04T09:29:49Z 2026-05-15 journal article Barrera, D., Nouisser, O., & Zerroudi, B. (2026). A Shepard-like Hermite interpolation operator with fourth approximation order. Journal of Computational and Applied Mathematics, 477(117158), 117158. https://doi.org/10.1016/j.cam.2025.117158 https://hdl.handle.net/10481/107731 10.1016/j.cam.2025.117158 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier