The paper presents some properties of Generalized T-splines (GT-splines), which are crucial to their actual application. In particular, the construction of a dual basis for a noteworthy class of GT-splines allows to show that, under suitable conditions, they form a partition of unity. Moreover, the paper contains a study of the approximation properties of the GT-spline space by constructing a class of quasi-interpolants which belong to it and are defined by using the dual basis.
On the approximation power of generalized T-splines / Bracco, Cesare; Cho, Durkbin; Dagnino, Catterina; Kim, Tae wan. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - STAMPA. - 311:(2017), pp. 423-438. [10.1016/j.cam.2016.07.011]
On the approximation power of generalized T-splines
BRACCO, CESARE;
2017
Abstract
The paper presents some properties of Generalized T-splines (GT-splines), which are crucial to their actual application. In particular, the construction of a dual basis for a noteworthy class of GT-splines allows to show that, under suitable conditions, they form a partition of unity. Moreover, the paper contains a study of the approximation properties of the GT-spline space by constructing a class of quasi-interpolants which belong to it and are defined by using the dual basis.
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