Univariate generalized splines are smooth piecewise functions with sections in certain extended Tchebycheff spaces. They are a natural extension of univariate (algebraic) polynomial splines, and enjoy the same structural properties as their polynomial counterparts. In this paper, we consider generalized spline spaces over planar T-meshes, and we deepen their parallelism with polynomial spline spaces over the same partitions. First, we extend the homological approach from polynomial to generalized splines. This provides some new insights into the dimension problem of a generalized spline space defined on a prescribed T-mesh for a given degree and smoothness. Second, we extend the construction of LR-splines to the generalized spline context.

Bracco, C., Lyche, T., Manni, C., Roman, F., Speleers, H. (2016). Generalized spline spaces over T-meshes: Dimension formula and locally refined generalized B-splines. APPLIED MATHEMATICS AND COMPUTATION, 272, 187-198 [10.1016/j.amc.2015.08.019].

Generalized spline spaces over T-meshes: Dimension formula and locally refined generalized B-splines

Manni C.;Speleers H.
2016-01-01

Abstract

Univariate generalized splines are smooth piecewise functions with sections in certain extended Tchebycheff spaces. They are a natural extension of univariate (algebraic) polynomial splines, and enjoy the same structural properties as their polynomial counterparts. In this paper, we consider generalized spline spaces over planar T-meshes, and we deepen their parallelism with polynomial spline spaces over the same partitions. First, we extend the homological approach from polynomial to generalized splines. This provides some new insights into the dimension problem of a generalized spline space defined on a prescribed T-mesh for a given degree and smoothness. Second, we extend the construction of LR-splines to the generalized spline context.
1-gen-2016
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/08 - ANALISI NUMERICA
English
Con Impact Factor ISI
Generalized splines; T-meshes; LR-meshes; Dimension formula
Bracco, C., Lyche, T., Manni, C., Roman, F., Speleers, H. (2016). Generalized spline spaces over T-meshes: Dimension formula and locally refined generalized B-splines. APPLIED MATHEMATICS AND COMPUTATION, 272, 187-198 [10.1016/j.amc.2015.08.019].
Bracco, C; Lyche, T; Manni, C; Roman, F; Speleers, H
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/215169
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