On the Local Approximation Power of Quasi-Hierarchical Powell-Sabin Splines

Speleers, Hendrik; Dierckx, Paul; Vandewalle, Stefan

doi:10.1007/978-3-642-11620-9_27

Cited by 4 publications

(3 citation statements)

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“…Besides the standard Hermite interpolant, several other quasi-interpolants of the form (20) have been proposed in the literature for Powell-Sabin splines, see [35,40,46]. Truncated hierarchical bases 1 based on Powell-Sabin B-splines have been previously presented in [47], and the local approximation power of the corresponding spaces has been investigated in [48] by exploiting hierarchical Hermite interpolants of the form (22).…”

Section: Remarkmentioning

confidence: 99%

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Effortless quasi-interpolation in hierarchical spaces

Speleers

Manni

2015

Numer. Math.

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We present a general and simple procedure to construct quasi-interpolants in hierarchical spaces, which are composed of a hierarchy of nested spaces. The hierarchical quasi-interpolants are described in terms of the truncated hierarchical basis. Once for each level in the hierarchy a quasi-interpolant is selected in the corresponding space, the hierarchical quasi-interpolants are obtained without any additional manipulation. The main properties of the quasi-interpolants selected at each level are preserved in the hierarchical construction. In particular, hierarchical local projectors are constructed, and the local approximation order of the underling hierarchical space is investigated. The presentation is detailed for the truncated hierarchical B-spline basis, and we discuss its extension to a more general framework.

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Section: Remarkmentioning

confidence: 99%

“…Note that the truncated hierarchical basis is called quasi-hierarchical basis in[47,48] 2. Basically this means that the spline space contains constants and that an appropriate blossom can be constructed therein.…”

mentioning

confidence: 99%

Effortless quasi-interpolation in hierarchical spaces

Speleers

Manni

2015

Numer. Math.

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“…They are both alternative bases for a hierarchical space build on a sequence of nested linear spaces. The notion of quasi-hierachical bases for hierarchical spaces has been introduced in [16,20] and also used in [29,30]. The concept of truncated bases has been described in [13,14].…”

Section: Introductionmentioning

confidence: 99%