A class of C2 quasi-interpolating splines free of Gibbs phenomenon
In many applications, it is useful to use piecewise polynomials that satisfy certain regularity conditions at the joint points. Cubic spline functions emerge as good candidates having C2 regularity. On the other hand, if the data points present discontinuities, the classical spline approximations pr...
| Autores: | , , , , |
|---|---|
| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2022 |
| País: | España |
| Recursos: | Universidad Politécnica de Cartagena(UPCT) |
| Repositório: | Repositorio Digital UPCT |
| OAI Identifier: | oai:repositorio.upct.es:10317/12228 |
| Acesso em linha: | http://hdl.handle.net/10317/12228 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Splines Adaption to discontinuities C2 regularity Quasi-interpolation Computer aided design (modeling of curves) Matemática Aplicada 12 Matemáticas |
| Resumo: | In many applications, it is useful to use piecewise polynomials that satisfy certain regularity conditions at the joint points. Cubic spline functions emerge as good candidates having C2 regularity. On the other hand, if the data points present discontinuities, the classical spline approximations produce Gibbs oscillations. In a recent paper, we have introduced a new nonlinear spline approximation avoiding the presence of these oscillations. Unfortunately, this new reconstruction loses the C2 regularity. This paper introduces a new nonlinear spline that preserves the regularity at all the joint points except at the end points of an interval containing a discontinuity, and that avoids the Gibbs oscillations. |
|---|