Existence and Uniqueness of Spaces of Splines of Maximal Pseudosmoothness

Dem’yanovich, Yu. K.; Kovtunenko, E. S.; Safonova, T. A.

doi:10.1007/s10958-017-3441-1

Cited by 2 publications

(3 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, the second technique is considered: the singularity is introduced into the spline approximation apparatus. When constructing splines, it has long been customary to use approximation relations, since they allow one to construct spaces of splines with the required approximation properties (see [2], [12] - [16], [20] - [27]). To refine the approximation of the required functions (for example, in the finite element method) and in the compression of information flows (for example, using wavelet decompositions), a chain of embedded spline spaces on embedded grids is required.…”

Section: Discussionmentioning

confidence: 99%

“…Remark 1. We would like to emphasize that formulas (22), (25) and (26) are valid for all t ∈ M because we can discuss the segment [c,d] (see (20)). If u ∈ U0, we write shortly ± u instead of − u and + u.…”

Section: Some Algebraic Identitiesmentioning

confidence: 99%

“…The notion of generalized continuity was introduced in [20]. In the aforementioned work, necessary and sufficient conditions for the pseudo-continuity of coordinate splines and their derivatives are obtained.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Wavelet Decomposition of the Singular Splines

2020

International Journal of Circuits, Systems and Signal Processing

View full text Add to dashboard Cite

One of the approaches to the problem of approximating functions with a singularity is the creation of an approximating apparatus based on splines with the same feature. For the wavelet decomposition of spline spaces it is important that the property of the embedding of these spaces is associated with embedding grids. The purpose of this paper is to consider ways of constructing spaces of splines with a predefined singularity and obtain their wavelet decomposition. Here the concept of generalized smoothness is used, within which the mentioned singularity is generalized smooth. This approach leads to the construction of a system of embedded spaces on embedded grids. A spline-wavelet decomposition of mentioned spaces is presented. Reconstruction formulas are done

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Some Algebraic Identitiesmentioning

confidence: 99%