Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 7, Pages 1236–1247 (Mi zvmmf10431)  

This article is cited in 5 scientific papers (total in 5 papers)

Splitting algorithms for the wavelet transform of first-degree splines on nonuniform grids

B. M. Shumilov

Tomsk State University of Architecture and Building

Abstract: For the splines of first degree with nonuniform knots, a new type of wavelets with a biased support is proposed. Using splitting with respect to the even and odd knots, a new wavelet decomposition algorithm in the form of the solution of a three-diagonal system of linear algebraic equations with respect to the wavelet coefficients is proposed. The application of the proposed implicit scheme to the point prediction of time series is investigated for the first time. Results of numerical experiments on the prediction accuracy and the compression of spline wavelet decompositions are presented.

Key words: multiresolution analysis (MRA), wavelets, first-degree splines, nonuniform measurements, orthogonality to polynomials, decomposition and reconstruction relations, prediction.

DOI: https://doi.org/10.7868/S0044466916070176

Full text: PDF file (304 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2016, 56:7, 1209–1219

Bibliographic databases:

UDC: 519.652.3
Received: 16.03.2014
Revised: 20.01.2016

Citation: B. M. Shumilov, “Splitting algorithms for the wavelet transform of first-degree splines on nonuniform grids”, Zh. Vychisl. Mat. Mat. Fiz., 56:7 (2016), 1236–1247; Comput. Math. Math. Phys., 56:7 (2016), 1209–1219

Citation in format AMSBIB
\Bibitem{Shu16}
\by B.~M.~Shumilov
\paper Splitting algorithms for the wavelet transform of first-degree splines on nonuniform grids
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2016
\vol 56
\issue 7
\pages 1236--1247
\mathnet{http://mi.mathnet.ru/zvmmf10431}
\crossref{https://doi.org/10.7868/S0044466916070176}
\elib{https://elibrary.ru/item.asp?id=26302233}
\transl
\jour Comput. Math. Math. Phys.
\yr 2016
\vol 56
\issue 7
\pages 1209--1219
\crossref{https://doi.org/10.1134/S0965542516070174}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000381223400002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84979763250}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf10431
  • http://mi.mathnet.ru/eng/zvmmf/v56/i7/p1236

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. M. Shumilov, “About semi-orthogonal spline-wavelets with derivatives, and the algorithm with splitting”, Num. Anal. Appl., 10:1 (2017), 90–100  mathnet  crossref  crossref  mathscinet  isi  elib
    2. Z. M. Sulaimanov, B. M. Shumilov, “A splitting algorithm for the wavelet transform of cubic splines on a nonuniform grid”, Comput. Math. Math. Phys., 57:10 (2017), 1577–1591  mathnet  crossref  crossref  isi  elib  elib
    3. I. A. Blatov, Yu. A. Gerasimova, I. V. Kartashevskii, “Primenenie splainovykh veivletov k dekorrelyatsii vremennykh ryadov”, Matem. modelirovanie, 30:6 (2018), 60–75  mathnet
    4. E. A. Kochegurova, D. U, “Realizatsiya rekursivnogo tsifrovogo filtra na osnove shtrafnogo P-splaina”, Kompyuternaya optika, 42:6 (2018), 1083–1092  mathnet  crossref
    5. A. A. Makarov, S. V. Makarova, “O bloke filtrov v splain-veivletnom preobrazovanii na neravnomernoi setke”, Sib. zhurn. vychisl. matem., 24:3 (2021), 299–311  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:197
    Full text:28
    References:37
    First page:16

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021