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One-Dimensional Polynomial Splines for Cubic Splines

  • Dhananjay Singh
  • Madhusudan Singh
  • Zaynidinov Hakimjon
Chapter
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

This paper outlines the methods of spline and outlines the best tools and their features for signal processing and analysis. Studies of spline functions indicate that algorithms generated with them are convenient for use in digital signal processors. This is because algorithmic computation of coefficients and algorithms of recovery of signals include operations like parallel additions, multiplication and multiplication with accumulation which are typical for digital processing of signals. An extensive analysis of existing hardware intended for digital processing indicated that architecture and availability of hardware implemented special multiplication commands, parallel accumulative multiplication at Harvard could allow wide use of modern digital signal processors for implementation of spline-recovery methods.

References

  1. 1.
    A.G. Akritas, S.D. Danielopoulos, On the complexity of algorithms for the translation of polynomials. Computing 24(1), 51–60 (1980).  https://doi.org/10.1007/BF02242791. (Springer)MathSciNetCrossRefGoogle Scholar
  2. 2.
    O. Sobrie, N. Gillis, V. Mousseau, M. Pirlot, UTA-poly and UTA-splines: additive value functions with polynomial marginals. Eur. J. Oper. Res. 264(2), 405–418, ISSN 0377-2217, (2018).  https://doi.org/10.1016/j.ejor.2017.03.021MathSciNetCrossRefGoogle Scholar
  3. 3.
    J. Goh, A.A. Majid, A.I.M. Ismail, Numerical method using cubic B-spline for the heat and wave equation. Comput. Math. Appl. 62(12) (December 2011), 4492–4498 (2011). http://dx.doi.org/10.1016/j.camwa.2011.10.028MathSciNetCrossRefGoogle Scholar
  4. 4.
    S. Jana, S. Ray, F. Durst, A numerical method to compute solidification and melting processes. Appl. Math. Model. 31(1), 93–119, ISSN 0307-904X, (2007).  https://doi.org/10.1016/j.apm.2005.08.012CrossRefGoogle Scholar
  5. 5.
    X. Jia, P. Ziegenhein, S.B. Jiang, GPU-based high-performance computing for radiation therapy. Phys. Med. Biol. 59(4), R151–R182, (2014). [PMC. Web. 21 (2018)]CrossRefGoogle Scholar
  6. 6.
    D. Inman, R. Elmore, B. Bush, A survey onVLSI architectures of lifting based 2D discrete wavelet transform. Build. Serv. Eng. Res. Technol. 36(5), 628–637 (2015).  https://doi.org/10.1177/0143624415573215CrossRefGoogle Scholar
  7. 7.
    C. Beccari, G. Casciola, L. Romani, Computation and modeling in piecewise Chebyshevian spline spaces. Numer. Anal., arXiv:1611.02068, (2016)Google Scholar
  8. 8.
    A. Grigorenko, S. Yaremchenko, Investigation of static and dynamic behavior of anisotropic inhomogeneous shallow shells by Spline approximation method. J. Civ. Eng. Manag. 15(1), 87–93 (2009).  https://doi.org/10.3846/1392-3730.2009.15.87-93CrossRefGoogle Scholar
  9. 9.
    C-G. Zhu, X-Y. Zhao, Self-intersections of rational Bézier curves. Graph. Model. 76(5) (September 2014), 312–320, (2014). http://dx.doi.org/10.1016/j.gmod.2014.04.001CrossRefGoogle Scholar

Copyright information

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Dhananjay Singh
    • 1
  • Madhusudan Singh
    • 2
  • Zaynidinov Hakimjon
    • 3
  1. 1.Department of Electronics EngineeringHankuk University of Foreign Studies (Global Campus)YonginKorea (Republic of)
  2. 2.School of Technology Studies, Endicott College of International StudiesWoosong UniversityDaejeonKorea (Republic of)
  3. 3.Head of Department of Information TechnologiesTashkent University of Information TechnologiesTashkentUzbekistan

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