Abstract:
In this paper, an implicit method of decomposition of 7-th degree Hermite splines to a series of “lazy” wavelets with displaced supports is investigated. A splitting algorithm for wavelet transforms of solving four five-diagonal systems of linear equations with a strict diagonal dominance in parallel is justified. Results of numerical experiments on exactness for polynomials and on compression of spline-wavelet decomposition are presented.
Citation:
B. M. Shumilov, “A splitting algorithm for wavelet transforms of the Hermite splines of the seventh degree”, Sib. Zh. Vychisl. Mat., 18:4 (2015), 453–467; Num. Anal. Appl., 8:4 (2015), 365–377
\Bibitem{Shu15}
\by B.~M.~Shumilov
\paper A splitting algorithm for wavelet transforms of the Hermite splines of the seventh degree
\jour Sib. Zh. Vychisl. Mat.
\yr 2015
\vol 18
\issue 4
\pages 453--467
\mathnet{http://mi.mathnet.ru/sjvm595}
\crossref{https://doi.org/10.15372/SJNM20150409}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3492926}
\elib{https://elibrary.ru/item.asp?id=24817590}
\transl
\jour Num. Anal. Appl.
\yr 2015
\vol 8
\issue 4
\pages 365--377
\crossref{https://doi.org/10.1134/S1995423915040096}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84948422783}
Linking options:
https://www.mathnet.ru/eng/sjvm595
https://www.mathnet.ru/eng/sjvm/v18/i4/p453
This publication is cited in the following 6 articles:
Boris M. Shumilov, “An Algorithm with the Even-odd Splitting of the Wavelet Transform of Non-Hermitian Splines of the Seventh Degree”, WSEAS TRANSACTIONS ON SIGNAL PROCESSING, 18 (2022), 25
Boris Shumilov, Studies in Systems, Decision and Control, 342, Cyber-Physical Systems: Design and Application for Industry 4.0, 2021, 33
Boris M. Shumilov, “An Algorithm with the Even-odd Splitting of the Wavelet Transform of Non-Hermitian Splines of the Seventh Degree, II”, EQUATIONS, 1 (2021), 17
B M Shumilov, “Zero and first-degree spline multiwavelets and parallel computing”, J. Phys.: Conf. Ser., 1715:1 (2021), 012006
Boris M. Shumilov, “Construction of an Effective Preconditioner for the Even-odd Splitting of Cubic Spline Wavelets”, WSEAS TRANSACTIONS ON MATHEMATICS, 20 (2021), 717
Boris M. Shumilov, Advanced Engineering Materials and Modeling, 2016, 435
Citation in format AMSBIB
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