On wavelet decomposition of the singular splines

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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

BibTeX

@article{8fd3abab61604de6b9313d42b293de81,

title = "On wavelet decomposition of the singular splines",

abstract = "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.",

keywords = "Generalized smoothness, Reconstruction formulas, Singular splines, Spline-wavelet decomposition",

author = "Demjanovich, {Yu. K.} and Evdokimova, {T. O.} and Ivancova, {O. N.} and Lebedinskii, {D. M.} and Ponomareva, {A. Y.}",

note = "Funding Information: ACKNOWLEDGMENT This work was partly supported by RFBR Grant 15-0108847. Publisher Copyright: {\textcopyright} 2020, North Atlantic University Union. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2020",

month = sep,

day = "21",

doi = "10.46300/9106.2020.14.73",

language = "English",

volume = "14",

pages = "571--579",

journal = "International Journal of Circuits, Systems and Signal Processing",

issn = "1998-4464",

publisher = "North Atlantic University Union NAUN",

}

RIS

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