Research output: Contribution to journal › Article › peer-review
On wavelet decomposition of the singular splines. / Demjanovich, Yu. K.; Evdokimova, T. O.; Ivancova, O. N.; Lebedinskii, D. M.; Ponomareva, A. Y.
In: International Journal of Circuits, Systems and Signal Processing, Vol. 14, 21.09.2020, p. 571-579.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - On wavelet decomposition of the singular splines
AU - Demjanovich, Yu. K.
AU - Evdokimova, T. O.
AU - Ivancova, O. N.
AU - Lebedinskii, D. M.
AU - Ponomareva, A. Y.
N1 - Funding Information: ACKNOWLEDGMENT This work was partly supported by RFBR Grant 15-0108847. Publisher Copyright: © 2020, North Atlantic University Union. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/9/21
Y1 - 2020/9/21
N2 - 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.
AB - 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.
KW - Generalized smoothness
KW - Reconstruction formulas
KW - Singular splines
KW - Spline-wavelet decomposition
UR - http://www.scopus.com/inward/record.url?scp=85092252523&partnerID=8YFLogxK
U2 - 10.46300/9106.2020.14.73
DO - 10.46300/9106.2020.14.73
M3 - Article
AN - SCOPUS:85092252523
VL - 14
SP - 571
EP - 579
JO - International Journal of Circuits, Systems and Signal Processing
JF - International Journal of Circuits, Systems and Signal Processing
SN - 1998-4464
ER -
ID: 70122333