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On Linear Spline Wavelets with Shifted Supports. / Makarova, Svetlana; Makarov, Anton.

Numerical Computations: Theory and Algorithms. ред. / Yaroslav D. Sergeyev; Dmitri E. Kvasov; Yaroslav D. Sergeyev; Dmitri E. Kvasov. Cham : Springer Nature, 2020. стр. 430-437 (Lecture Notes in Computer Science; Том 11974 ).

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Harvard

Makarova, S & Makarov, A 2020, On Linear Spline Wavelets with Shifted Supports. в YD Sergeyev, DE Kvasov, YD Sergeyev & DE Kvasov (ред.), Numerical Computations: Theory and Algorithms. Lecture Notes in Computer Science, Том. 11974 , Springer Nature, Cham, стр. 430-437, 3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019, Crotone, Италия, 15/06/19. https://doi.org/10.1007/978-3-030-40616-5_40

APA

Makarova, S., & Makarov, A. (2020). On Linear Spline Wavelets with Shifted Supports. в Y. D. Sergeyev, D. E. Kvasov, Y. D. Sergeyev, & D. E. Kvasov (Ред.), Numerical Computations: Theory and Algorithms (стр. 430-437). (Lecture Notes in Computer Science; Том 11974 ). Springer Nature. https://doi.org/10.1007/978-3-030-40616-5_40

Vancouver

Makarova S, Makarov A. On Linear Spline Wavelets with Shifted Supports. в Sergeyev YD, Kvasov DE, Sergeyev YD, Kvasov DE, Редакторы, Numerical Computations: Theory and Algorithms. Cham: Springer Nature. 2020. стр. 430-437. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-030-40616-5_40

Author

Makarova, Svetlana ; Makarov, Anton. / On Linear Spline Wavelets with Shifted Supports. Numerical Computations: Theory and Algorithms. Редактор / Yaroslav D. Sergeyev ; Dmitri E. Kvasov ; Yaroslav D. Sergeyev ; Dmitri E. Kvasov. Cham : Springer Nature, 2020. стр. 430-437 (Lecture Notes in Computer Science).

BibTeX

@inproceedings{de492087f2e64904a4e6f682d66e39c3,
title = "On Linear Spline Wavelets with Shifted Supports",
abstract = "We examine Faber{\textquoteright}s type decompositions for spaces of linear minimal splines constructed on nonuniform grids on a segment. A characteristic feature of the Faber decomposition is that the basis wavelets are centered around the knots that do not belong to the coarse grid. The construction of the lazy wavelets begins with the use of the basis functions in refined spline space centered at the odd knots. We propose to use as wavelets the functions centered at the even knots under some conditions. In contrast to lazy wavelets, in this case the decomposition system of equations has a unique solution, which can be found by the sweep method with the guarantee of well-posedness and stability.",
keywords = "B-spline, Minimal splines, Nonuniform grid, Wavelets, ALGORITHMS",
author = "Svetlana Makarova and Anton Makarov",
note = "Makarova S., Makarov A. (2020) On Linear Spline Wavelets with Shifted Supports. In: Sergeyev Y., Kvasov D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science, vol 11974. Springer, Cham; 3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019 ; Conference date: 15-06-2019 Through 21-06-2019",
year = "2020",
doi = "10.1007/978-3-030-40616-5_40",
language = "English",
isbn = "9783030406158",
series = "Lecture Notes in Computer Science",
publisher = "Springer Nature",
pages = "430--437",
editor = "Sergeyev, {Yaroslav D.} and Kvasov, {Dmitri E.} and Sergeyev, {Yaroslav D.} and Kvasov, {Dmitri E.}",
booktitle = "Numerical Computations: Theory and Algorithms",
address = "Germany",

}

RIS

TY - GEN

T1 - On Linear Spline Wavelets with Shifted Supports

AU - Makarova, Svetlana

AU - Makarov, Anton

N1 - Makarova S., Makarov A. (2020) On Linear Spline Wavelets with Shifted Supports. In: Sergeyev Y., Kvasov D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science, vol 11974. Springer, Cham

PY - 2020

Y1 - 2020

N2 - We examine Faber’s type decompositions for spaces of linear minimal splines constructed on nonuniform grids on a segment. A characteristic feature of the Faber decomposition is that the basis wavelets are centered around the knots that do not belong to the coarse grid. The construction of the lazy wavelets begins with the use of the basis functions in refined spline space centered at the odd knots. We propose to use as wavelets the functions centered at the even knots under some conditions. In contrast to lazy wavelets, in this case the decomposition system of equations has a unique solution, which can be found by the sweep method with the guarantee of well-posedness and stability.

AB - We examine Faber’s type decompositions for spaces of linear minimal splines constructed on nonuniform grids on a segment. A characteristic feature of the Faber decomposition is that the basis wavelets are centered around the knots that do not belong to the coarse grid. The construction of the lazy wavelets begins with the use of the basis functions in refined spline space centered at the odd knots. We propose to use as wavelets the functions centered at the even knots under some conditions. In contrast to lazy wavelets, in this case the decomposition system of equations has a unique solution, which can be found by the sweep method with the guarantee of well-posedness and stability.

KW - B-spline

KW - Minimal splines

KW - Nonuniform grid

KW - Wavelets

KW - ALGORITHMS

UR - http://www.scopus.com/inward/record.url?scp=85080873764&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/d3d81c08-77db-3198-b6bb-3f39d610f509/

U2 - 10.1007/978-3-030-40616-5_40

DO - 10.1007/978-3-030-40616-5_40

M3 - Conference contribution

AN - SCOPUS:85080873764

SN - 9783030406158

T3 - Lecture Notes in Computer Science

SP - 430

EP - 437

BT - Numerical Computations: Theory and Algorithms

A2 - Sergeyev, Yaroslav D.

A2 - Kvasov, Dmitri E.

A2 - Sergeyev, Yaroslav D.

A2 - Kvasov, Dmitri E.

PB - Springer Nature

CY - Cham

T2 - 3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019

Y2 - 15 June 2019 through 21 June 2019

ER -

ID: 52285108