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Ukrainian Mathematical Journal

, Volume 70, Issue 9, pp 1375–1394 | Cite as

Magic Efficiency of the Approximation of Smooth Functions by Weighted Means of Two N-Point Padé Approximants

  • R. Jedynak
  • J. Gilewicz
Article
  • 23 Downloads

We consider the approximation of smooth functions by two weighted N-point Padé approximants and present some numerical examples and the inequalities between the Stieltjes function and its N-point Padé approximant.

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References

  1. 1.
    V. Barsan and V. Kuncser, “Exact and approximate analytical solutions of Weiss equation of ferromagnetism and their experimental relevance,” Philos. Mag. Lett., 97, 359–371 (2017).CrossRefGoogle Scholar
  2. 2.
    B. Brodnik Zugelj and M. Kalin, “Submicron-scale experimental and theoretical analyses of multi-asperity contacts with different roughnesses,” Tribology Int., 119, 667–671 (2017).CrossRefGoogle Scholar
  3. 3.
    A. Cohen, “A Padé approximant to the inverse Langevin function,” Rheologica Acta, 30, Issue 3, 270–273 (1991).CrossRefGoogle Scholar
  4. 4.
    E. Darabi and M. Itskov, A simple and accurate approximation of the inverse Langevin function,” Rheologica Acta, 54, Issue 5, 455–459 (2015).CrossRefGoogle Scholar
  5. 5.
    J. Gilewicz, “Approximants de Padé,” Lect. Notes Math., 667 (1978).Google Scholar
  6. 6.
    J. Gilewicz, “100 years of improvements of bounding properties of one-point, two-point and N-point Padé approximants to the Stieltjes functions,” Appl. Numer. Math., 60, 1320–1331 (2010).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    J. Gilewicz, M. Pindor, S. Tokarzewski, and J. J. Telega, “N-point Padé approximants and two sided estimates of errors on the real axis for the Stieltjes functions,” J. Comput. Appl. Math., 178, 247–253 (2005).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    J. Gilewicz and R. Jedynak, “Compatibility of continued fraction convergents with Padé approximants,” in: Approximation and Computation. In Honor of Gradimir Milovanović. Most Papers Based on the Presentations at the International Conference, Niš, Serbia, August 25–29, 2008: Springer Optim. and Appl., Springer-Verlag (2010), pp. 135–144.Google Scholar
  9. 9.
    A. P. Holub and L. O. Lysenko, “Padé approximants for some classes of multivariate functions,” Ukr. Mat. Zh., 69, No. 5, 631–640 (2017); English translation : Ukr. Mat. J., 69, No. 5, 734–745 (2017).Google Scholar
  10. 10.
    R. Jedynak, “Approximation of the inverse Langevin function revisited,” Rheologica Acta, 54, Issue 1, 29–39 (2015).CrossRefGoogle Scholar
  11. 11.
    R. Jedynak, “New facts concerning the approximation of the inverse Langevin function,” J. Non-Newton. Fluid Mech., 249 (2017).Google Scholar
  12. 12.
    R. Jedynak and J. Gilewicz, “Approximation of the integrals of the Gaussian distribution of asperity heights in the Greenwood–Tripp contact model of two rough surfaces revisited,” J. Appl. Math., 2013 (2013), Article ID 459280.Google Scholar
  13. 13.
    R. Jedynak and J. Gilewicz, “Approximation of smooth functions by weighted means of N-point Padé approximants,” Ukr. Math. Zh., 65, No. 10, 1410–1419 (2014); English translation : Ukr. Math. J., 65, No. 10, 1566–1576 (2014).Google Scholar
  14. 14.
    R. Jedynak and J. Gilewicz, “Computation of the c-table related to the Padé approximation,” J. Appl. Math., 2013 (2013), Article ID 185648.Google Scholar
  15. 15.
    R. Jedynak and M. Sulek, “Numerical and experimental investigation of plastic interaction between rough surfaces,” Arab. J. Sci. Eng., 39, 4165–4177 (2014).CrossRefGoogle Scholar
  16. 16.
    M. Kröger, “Simple, admissible, and accurate approximants of the inverse Langevin and Brillouin functions, relevant for strong polymer deformations and flows,” J. Non-Newton Fluid Mech., 223, 77–87 (2015).MathSciNetCrossRefGoogle Scholar
  17. 17.
    O. M. Lytvyn and V. L. Rvachev, Taylor’s Classical Formula, Its Generalization and Application [in Ukrainian], Naukova Dumka, Kiev (1973).Google Scholar
  18. 18.
    N. Lorenz, G. Offner, and O. Knaus, “Fast thermo-elasto-hydrodynamic modeling approach for mixed lubricated journal bearings in internal combustion engines,” Proc. Inst. Mech. Eng., J. Pt J.: Eng. Tribol., 229, 962–976 (2015).CrossRefGoogle Scholar
  19. 19.
    B. C. Marchi and E. M. Arruda, “An error-minimizing approach to inverse Langevin approximations,” Rheol. Acta, 54, 887–902 (2015).CrossRefGoogle Scholar
  20. 20.
    J. Takacs, “Approximations for Brillouin and its reverse function,” COMPEL — Int. J. Comput. Math. Electr. Electron. Eng., 35, Issue 6, 2095–2099 (2016).CrossRefGoogle Scholar
  21. 21.
    J. Takacs, Hysteresis loop reversing by applying Langevin approximation,” COMPEL—Int. J. Comput. Math. Electr. Electron. Eng., 36, Issue 4, 850–858 (2017).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • R. Jedynak
    • 1
  • J. Gilewicz
    • 1
  1. 1.K. Pulaski University of Technology and HumanitiesRadomPoland

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