Analysis of a new nonlinear interpolatory subdivision scheme on σ quasi-uniform grids

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 piecewi...

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Detalhes bibliográficos
Autores: Ortiz Herranz, Pedro, Trillo Moya, Juan Carlos
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Recursos:Universidad Politécnica de Cartagena(UPCT)
Repositorio:Repositorio Digital UPCT
OAI Identifier:oai:repositorio.upct.es:10317/10478
Acesso em linha:http://hdl.handle.net/10317/10478
https://www.mdpi.com/2227-7390/9/12/1320
Access Level:acceso abierto
Palavra-chave:Interpolation
Subdivision schemes
Nonlinearity
Nonuniform
σ quasi-uniform
Matemática Aplicada
12 Matemáticas
Descrição
Resumo: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 s quasi-uniform grids. We also perform some numerical experiments to reinforce the theoretical results.