Standard

On splines’ smoothness. / Dem’yanovich, Yu K.; Miroshnichenko, I. D.; Musafarova, E. F.

In: WSEAS Transactions on Mathematics, Vol. 18, 01.01.2019, p. 129-136.

Research output: Contribution to journal › Article › peer-review

Harvard

Dem’yanovich, YK, Miroshnichenko, ID & Musafarova, EF 2019, 'On splines’ smoothness', WSEAS Transactions on Mathematics, vol. 18, pp. 129-136.

APA

Dem’yanovich, Y. K., Miroshnichenko, I. D., & Musafarova, E. F. (2019). On splines’ smoothness. WSEAS Transactions on Mathematics, 18, 129-136.

Vancouver

Dem’yanovich YK, Miroshnichenko ID, Musafarova EF. On splines’ smoothness. WSEAS Transactions on Mathematics. 2019 Jan 1;18:129-136.

Author

Dem’yanovich, Yu K. ; Miroshnichenko, I. D. ; Musafarova, E. F. / On splines’ smoothness. In: WSEAS Transactions on Mathematics. 2019 ; Vol. 18. pp. 129-136.

BibTeX

@article{049bf07cd5de4fb98b856c438bce3933,
title = "On splines{\textquoteright} smoothness",
abstract = "The aim of this article is to discuss the generalized smoothness for the splines on q-covered manifold, where q is the natural number. By using mentioned smoothness it is possible to consider the different types of smoothness, for example, the integral smoothness, the weight smoothness, the derivatives smoothness, etc. We find the necessary and sufficient conditions for calculation of basic splines with a{\textquoteright}priori prescribed smoothness. The mentioned smoothness may contain no more than q (locally formulated) linearly independentconditions. If the number of the conditions is exactly q, then the discussed spline spaces on the embedded grids are also embedded.",
keywords = "Embedded spaces, Generalized smoothness, Key–Words: approximation relations, Wavelet expansions",
author = "Dem{\textquoteright}yanovich, {Yu K.} and Miroshnichenko, {I. D.} and Musafarova, {E. F.}",
year = "2019",
month = jan,
day = "1",
language = "English",
volume = "18",
pages = "129--136",
journal = "WSEAS Transactions on Mathematics",
issn = "1109-2769",
publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - On splines’ smoothness

AU - Dem’yanovich, Yu K.

AU - Miroshnichenko, I. D.

AU - Musafarova, E. F.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The aim of this article is to discuss the generalized smoothness for the splines on q-covered manifold, where q is the natural number. By using mentioned smoothness it is possible to consider the different types of smoothness, for example, the integral smoothness, the weight smoothness, the derivatives smoothness, etc. We find the necessary and sufficient conditions for calculation of basic splines with a’priori prescribed smoothness. The mentioned smoothness may contain no more than q (locally formulated) linearly independentconditions. If the number of the conditions is exactly q, then the discussed spline spaces on the embedded grids are also embedded.

AB - The aim of this article is to discuss the generalized smoothness for the splines on q-covered manifold, where q is the natural number. By using mentioned smoothness it is possible to consider the different types of smoothness, for example, the integral smoothness, the weight smoothness, the derivatives smoothness, etc. We find the necessary and sufficient conditions for calculation of basic splines with a’priori prescribed smoothness. The mentioned smoothness may contain no more than q (locally formulated) linearly independentconditions. If the number of the conditions is exactly q, then the discussed spline spaces on the embedded grids are also embedded.

KW - Embedded spaces

KW - Generalized smoothness

KW - Key–Words: approximation relations

KW - Wavelet expansions

UR - http://www.scopus.com/inward/record.url?scp=85067335078&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85067335078

VL - 18

SP - 129

EP - 136

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

ER -

ID: 53483738