Advertisement

Parabolic Splines based One-Dimensional Polynomial

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

Abstract

Chapter  1 mentioned that the functions that are glued from various pieces of polynomials on a fixed system are called splines. The obtained smooth homogeneous structure piecewise-polynomial functions (compilation from polynomials of the same degree) are called spline functions or simply splines. The broken spline function is the simplest and historical example of splines. Spline functions are a developing field of the function approximation and digital analysis theory.

References

  1. 1.
    M. Antonelli, C. Beccari, G. Casciola, A general framework for the construction of piecewise-polynomial local interpolants of minimum degree. Adv. Comput. Math. (2013).  https://doi.org/10.1007/s10444-013-9335-y MathSciNetCrossRefGoogle Scholar
  2. 2.
    C.V. Beccari, G. Casciola, S. Morigi, On multi-degree splines. Comput. Aided Geom. Des. 58 (2017).  https://doi.org/10.1016/j.cagd.2017.10.003MathSciNetCrossRefGoogle Scholar
  3. 3.
    F. Johnson, M.F. Hutchinson, C. The, C. Beesley, J. Green, Topographic relationships for design rainfalls over Australia. J. Hydrol. 533, 439–451 (2016). ISSN 0022-1694,  https://doi.org/10.1016/j.jhydrol.2015.12.035CrossRefGoogle Scholar
  4. 4.
  5. 5.
    D. Singh, H. Zaynidinov, H.J. Lee, Piecewise-quadratic Harmut basis funictions and their application to problem in digital signal processing. Int. J. Commun. Syst. 23, 751–762 (2010). (www.interscience.wiley.com).  https://doi.org/10.1002/dac.1093
  6. 6.
    W. Wang, Special quadratic quadrilateral finite elements for local refinement with irregular nodes. Comput. Methods Appl. Mech. Eng. 182(1–2), 109–134 (2000). ISSN 0045-7825.  https://doi.org/10.1016/S0045-7825(99)00088-2MathSciNetCrossRefGoogle Scholar
  7. 7.
    Y.V. Zakharov, T. Tozer, Local spline approximation of time-varying channel model. Electron. Lett. 37, 1408–1409 (2001).  https://doi.org/10.1049/el:20010942CrossRefGoogle Scholar
  8. 8.
    B.I. Kvasov, Parabolic B-splines in interpolation problems. USSR Comput. Math. Math. Phys. 23(2), 13–19 (1983). ISSN 0041-5553.  https://doi.org/10.1016/S0041-5553(83)80041-XCrossRefGoogle Scholar
  9. 9.
    S. Gao, Z. Zhang, C. Cao, Differentiation and numerical integral of the cubic spline interpolation. J. Comput. 6(10), 2037–2044 (2011)Google Scholar
  10. 10.
    T. Blu, M. Unser, Wavelets, fractals, and radial basis functions. IEEE Trans. Signal Process. 50(3), 543–553 (2002)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Y. Lipman, D. Levin, D. Cohen-Or, Green Coordinates. In ACM SIGGRAPH 2008 papers (SIGGRAPH ’08). ACM, New York, NY, USA, Article 78, 10 pp (2008).  https://doi.org/10.1145/1399504.1360677
  12. 12.
    B. Mohandes, Y.L. Abdelmagid, I. Boiko, Development of PSS tuning rules using multi-objective optimization. Int. J. Electr. Power Energy Syst. 100, 449–462 (2018). ISSN 0142-0615.  https://doi.org/10.1016/j.ijepes.2018.01.041CrossRefGoogle Scholar
  13. 13.
    M. Walz, T. Zebrowski, J. Küchenmeister, K. Busch, B-spline modal method: a polynomial approach compared to the Fourier modal method. Opt. Express 21(12), 14683–14697 (2013)CrossRefGoogle Scholar
  14. 14.
    O. Hidayov, D. Singh, B. G.B. Gwak, S-Y. Young, A Simulink-model of specialized processor on the piecewise-polynomial bases. International Conference on Advanced Communication Technology, ICACT (2011)Google Scholar
  15. 15.
    G. Canan Hazar, M. Ali Sarıgöl, Acta Appl. Math. 154, 153 (2018).  https://doi.org/10.1007/s10440-017-0138-xMathSciNetCrossRefGoogle 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

Personalised recommendations