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On de Boor–Fix Type Functionals for Minimal Splines. / Kulikov, Egor K.; Makarov, Anton A.

Topics in Classical and Modern Analysis. ред. / M. Abell; E. Iacob; A. Stokolos; S. Taylor; S. Tikhonov; J. Zhu. Cham : Springer Nature, 2019. стр. 211-225 (Applied and Numerical Harmonic Analysis).

Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › Рецензирование

Harvard

Kulikov, EK & Makarov, AA 2019, On de Boor–Fix Type Functionals for Minimal Splines. в M Abell, E Iacob, A Stokolos, S Taylor, S Tikhonov & J Zhu (ред.), Topics in Classical and Modern Analysis. Applied and Numerical Harmonic Analysis, Springer Nature, Cham, стр. 211-225. https://doi.org/10.1007/978-3-030-12277-5_13

APA

Kulikov, E. K., & Makarov, A. A. (2019). On de Boor–Fix Type Functionals for Minimal Splines. в M. Abell, E. Iacob, A. Stokolos, S. Taylor, S. Tikhonov, & J. Zhu (Ред.), Topics in Classical and Modern Analysis (стр. 211-225). (Applied and Numerical Harmonic Analysis). Springer Nature. https://doi.org/10.1007/978-3-030-12277-5_13

Vancouver

Kulikov EK, Makarov AA. On de Boor–Fix Type Functionals for Minimal Splines. в Abell M, Iacob E, Stokolos A, Taylor S, Tikhonov S, Zhu J, Редакторы, Topics in Classical and Modern Analysis. Cham: Springer Nature. 2019. стр. 211-225. (Applied and Numerical Harmonic Analysis). https://doi.org/10.1007/978-3-030-12277-5_13

Author

Kulikov, Egor K. ; Makarov, Anton A. / On de Boor–Fix Type Functionals for Minimal Splines. Topics in Classical and Modern Analysis. Редактор / M. Abell ; E. Iacob ; A. Stokolos ; S. Taylor ; S. Tikhonov ; J. Zhu. Cham : Springer Nature, 2019. стр. 211-225 (Applied and Numerical Harmonic Analysis).

BibTeX

@inbook{d72a94ad54574e7cbee5facfac082469,
title = "On de Boor–Fix Type Functionals for Minimal Splines",
abstract = "This paper considers minimal coordinate splines. These splines as a special case include well-known polynomial B-splines and share most properties of B-splines (linear independency, smoothness, nonnegativity, etc.). We construct a system of dual functionals biorthogonal to the system of minimal splines. The obtained results are illustrated with an example of a polynomial generating vector function, which leads to the construction of B-splines and the de Boor–Fix functionals. For nonpolynomial generating vector functions we give formulas for the construction of nonpolynomial splines and the dual de Boor–Fix type functionals.",
keywords = "Approximation functional, B-spline, Biorthogonal system, de Boor–Fix functional, Dual functional, Minimal spline, Nonpolynomial spline",
author = "Kulikov, {Egor K.} and Makarov, {Anton A.}",
note = "Kulikov E.K., Makarov A.A. (2019) On de Boor–Fix Type Functionals for Minimal Splines. In: Abell M., Iacob E., Stokolos A., Taylor S., Tikhonov S., Zhu J. (eds) Topics in Classical and Modern Analysis. Applied and Numerical Harmonic Analysis. Birkh{\"a}user, Cham",
year = "2019",
month = nov,
day = "20",
doi = "10.1007/978-3-030-12277-5_13",
language = "English",
isbn = "9783030122768",
series = "Applied and Numerical Harmonic Analysis",
publisher = "Springer Nature",
pages = "211--225",
editor = "M. Abell and E. Iacob and A. Stokolos and S. Taylor and S. Tikhonov and J. Zhu",
booktitle = "Topics in Classical and Modern Analysis",
address = "Germany",

}

RIS

TY - CHAP

T1 - On de Boor–Fix Type Functionals for Minimal Splines

AU - Kulikov, Egor K.

AU - Makarov, Anton A.

N1 - Kulikov E.K., Makarov A.A. (2019) On de Boor–Fix Type Functionals for Minimal Splines. In: Abell M., Iacob E., Stokolos A., Taylor S., Tikhonov S., Zhu J. (eds) Topics in Classical and Modern Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham

PY - 2019/11/20

Y1 - 2019/11/20

N2 - This paper considers minimal coordinate splines. These splines as a special case include well-known polynomial B-splines and share most properties of B-splines (linear independency, smoothness, nonnegativity, etc.). We construct a system of dual functionals biorthogonal to the system of minimal splines. The obtained results are illustrated with an example of a polynomial generating vector function, which leads to the construction of B-splines and the de Boor–Fix functionals. For nonpolynomial generating vector functions we give formulas for the construction of nonpolynomial splines and the dual de Boor–Fix type functionals.

AB - This paper considers minimal coordinate splines. These splines as a special case include well-known polynomial B-splines and share most properties of B-splines (linear independency, smoothness, nonnegativity, etc.). We construct a system of dual functionals biorthogonal to the system of minimal splines. The obtained results are illustrated with an example of a polynomial generating vector function, which leads to the construction of B-splines and the de Boor–Fix functionals. For nonpolynomial generating vector functions we give formulas for the construction of nonpolynomial splines and the dual de Boor–Fix type functionals.

KW - Approximation functional

KW - B-spline

KW - Biorthogonal system

KW - de Boor–Fix functional

KW - Dual functional

KW - Minimal spline

KW - Nonpolynomial spline

UR - http://www.scopus.com/inward/record.url?scp=85074656630&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/boorfix-type-functionals-minimal-splines

U2 - 10.1007/978-3-030-12277-5_13

DO - 10.1007/978-3-030-12277-5_13

M3 - Chapter

AN - SCOPUS:85074656630

SN - 9783030122768

T3 - Applied and Numerical Harmonic Analysis

SP - 211

EP - 225

BT - Topics in Classical and Modern Analysis

A2 - Abell, M.

A2 - Iacob, E.

A2 - Stokolos, A.

A2 - Taylor, S.

A2 - Tikhonov, S.

A2 - Zhu, J.

PB - Springer Nature

CY - Cham

ER -

ID: 49050139