A class of C2 quasi-interpolating splines free of Gibbs phenomenon
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AuthorAmat Plata, Sergio; Levin, David; Ruiz Álvarez, Juan; Trillo Moya, Juan Carlos; Yáñez Avendaño, Dionisio Félix
Knowledge AreaMatemática Aplicada
SponsorsOpen Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work was funded by the Programa de Apoyo a la investigación de la fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 20928/PI/18, by the national research project MMTM2015-64382-P and PID2019-108336GB-I00 (MINECO/FEDER), by grant MTM2017-83942 funded by Spanish MINECO and by grant PID2020-117211GB-I00 funded by MCIN/AEI/10.13039/501100011033.
Realizado en/conUniversidad Politécnica de Cartagena; Universidad de Valencia
Bibliographic CitationAmat, S., Levin, D., Ruiz-Álvarez, J. et al. A class of C2 quasi-interpolating splines free of Gibbs phenomenon. Numer Algor 91, 51–79 (2022). https://doi.org/10.1007/s11075-022-01254-6
Adaption to discontinuities
Computer aided design (modeling of curves)
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.
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