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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. ed. / M. Abell; E. Iacob; A. Stokolos; S. Taylor; S. Tikhonov; J. Zhu. Cham : Springer Nature, 2019. p. 211-225 (Applied and Numerical Harmonic Analysis).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Harvard

Kulikov, EK & Makarov, AA 2019, On de Boor–Fix Type Functionals for Minimal Splines. in M Abell, E Iacob, A Stokolos, S Taylor, S Tikhonov & J Zhu (eds), Topics in Classical and Modern Analysis. Applied and Numerical Harmonic Analysis, Springer Nature, Cham, pp. 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. In M. Abell, E. Iacob, A. Stokolos, S. Taylor, S. Tikhonov, & J. Zhu (Eds.), Topics in Classical and Modern Analysis (pp. 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. In Abell M, Iacob E, Stokolos A, Taylor S, Tikhonov S, Zhu J, editors, Topics in Classical and Modern Analysis. Cham: Springer Nature. 2019. p. 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. editor / M. Abell ; E. Iacob ; A. Stokolos ; S. Taylor ; S. Tikhonov ; J. Zhu. Cham : Springer Nature, 2019. pp. 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