Progressive iterative Schoenberg-Marsden variation diminishing operator and related quadratures

In this paper we propose an approximation method based on the classical Schoenberg-Marsden variation diminishing operator with applications to the construction of new quadrature rules. We compare the new operator with the multilevel one studied in [E. Fornaca, P. Lamberti: Multilevel Schoenberg-Marsden variation diminishing operator and related quadratures, J. Comput. Appl. Math., 445 (2024), Article 115804, 10.1016/j.cam.2024.115804] in order to characterize both of them with respect to the well known classical one. We discuss convergence properties and present numerical experiments.