Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
Singular splines. / Dem'yanovich, Yu K.; Evdokimova, T. O.; Ivantsova, O. N.; Lebedinskii, D. M.; Ponomareva, A. Y.
International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019. ed. / Theodore E. Simos; Theodore E. Simos; Theodore E. Simos; Theodore E. Simos; Theodore E. Simos; Charalambos Tsitouras. American Institute of Physics, 2020. 420029 (AIP Conference Proceedings; Vol. 2293).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
}
TY - GEN
T1 - Singular splines
AU - Dem'yanovich, Yu K.
AU - Evdokimova, T. O.
AU - Ivantsova, O. N.
AU - Lebedinskii, D. M.
AU - Ponomareva, A. Y.
N1 - Funding Information: This work was partly supported by RFBR Grant 15-01-08847,20-51-54002. Publisher Copyright: © 2020 American Institute of Physics Inc.. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/11/24
Y1 - 2020/11/24
N2 - Singular splines are required for approximation of functions with point singularities. This paper develops a concept ofgeneralized smoothness in the case of the mentioned splines. Generalized smoothness is defined as equality of values for two functionals with local supports. The splines are constructed by the suitable approximation relations. The last ones are obtained by application of the concept to the right part of the relations (i.e. to generating vector function). Sufficient conditions of coordinate spline existence are established. The generalized smoothness of the coordinate splines has as a consequence of embedded spline spaces constructed on embedded grids.
AB - Singular splines are required for approximation of functions with point singularities. This paper develops a concept ofgeneralized smoothness in the case of the mentioned splines. Generalized smoothness is defined as equality of values for two functionals with local supports. The splines are constructed by the suitable approximation relations. The last ones are obtained by application of the concept to the right part of the relations (i.e. to generating vector function). Sufficient conditions of coordinate spline existence are established. The generalized smoothness of the coordinate splines has as a consequence of embedded spline spaces constructed on embedded grids.
UR - http://www.scopus.com/inward/record.url?scp=85097990808&partnerID=8YFLogxK
U2 - 10.1063/5.0031734
DO - 10.1063/5.0031734
M3 - Conference contribution
AN - SCOPUS:85097990808
T3 - AIP Conference Proceedings
BT - International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019
A2 - Simos, Theodore E.
A2 - Simos, Theodore E.
A2 - Simos, Theodore E.
A2 - Simos, Theodore E.
A2 - Simos, Theodore E.
A2 - Tsitouras, Charalambos
PB - American Institute of Physics
T2 - International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019
Y2 - 23 September 2019 through 28 September 2019
ER -
ID: 74275678