Analysis of a New Nonlinear Interpolatory Subdivision Scheme on ? Quasi-Uniform Grids

Pedro Ortiz and Juan Carlos Trillo
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Pedro Ortiz: Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain
Juan Carlos Trillo: Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain

Mathematics, 2021, vol. 9, issue 12, 1-23

Abstract: In this paper, we introduce and analyze the behavior of a nonlinear subdivision operator called PPH, which comes from its associated PPH nonlinear reconstruction operator on nonuniform grids. The acronym PPH stands for Piecewise Polynomial Harmonic, since the reconstruction is built by using piecewise polynomials defined by means of an adaption based on the use of the weighted Harmonic mean. The novelty of this work lies in the generalization of the already existing PPH subdivision scheme to the nonuniform case. We define the corresponding subdivision scheme and study some important issues related to subdivision schemes such as convergence, smoothness of the limit function, and preservation of convexity. In order to obtain general results, we consider ? quasi-uniform grids. We also perform some numerical experiments to reinforce the theoretical results.

Keywords: interpolation; subdivision schemes; nonlinearity; nonuniform; ? quasi-uniform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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