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...

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Detalhes bibliográficos
Autores: Amat Plata, Sergio, Levin, David, Ruiz Álvarez, Juan, Trillo Moya, Juan Carlos, Yáñez Avendaño, Dionisio Félix
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
Descrição
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.