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...
| Autores: | , |
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| 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 |
| 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. |
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