Ukrainian Mathematical Journal

, Volume 66, Issue 6, pp 905–915 | Cite as

Estimation of the Remainder for the Interpolation Continued C-Fraction

  • M. M. Pahirya
Article
  • 22 Downloads

We estimate the remainder of the interpolation continued C-fraction.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    I. P. Havrylyuk and V. L. Makarov, Numerical Methods, Part 1 [in Ukrainian], Vyshcha Shkola, Kyiv (1995).Google Scholar
  2. 2.
    A. A. Privalov, Theory of Interpolation of Functions [in Russian], Saratov University, Saratov (1990).Google Scholar
  3. 3.
    G. A. Baker, Jr., and P. Graves-Morris, Padé Approximants, Addison-Wesley, London (1981).Google Scholar
  4. 4.
    V. Ya. Skorobogat’ko, Theory of Branching Continued Fractions and Its Application in Numerical Mathematics [in Russian], Nauka, Kiev (1983).Google Scholar
  5. 5.
    J. M. Hoene-Wroński, Introduction à la Philosophie des Mathématiques et Technie de l’Algorithmique, Courcier, Paris (1811).Google Scholar
  6. 6.
    J. M. Hoene-Wroński, Philosophie de la Technie Algorithmique: Loi Suprême et Universelle des Mathématiques, de L’imprimerie de P. Didot L’Aine, Paris (1815–1817).Google Scholar
  7. 7.
    T. N. Thiele, Interpolationsprechnung, Commisission von B. G. Teubner, Leipzig (1909).Google Scholar
  8. 8.
    L. M. Milne-Thomson, The Calculus of Finite Differences, MacMillan, London (1933).Google Scholar
  9. 9.
    M. M. Pahirya, “On the efficiency of approximation of functions by some types of interpolation continued fractions,” Mat. Met. Fiz.-Mekh. Polya, 46, No. 4, 57–64 (2003).MathSciNetGoogle Scholar
  10. 10.
    M. M. Pahirya, “Evaluation of the remainder term for the Thiele interpolation continued faction,” Ukr. Mat. Zh., 60, No. 11, 1548–1554 (2008); English translation: Ukr. Math. J., 60, No. 11, 1813–1822 (2008).Google Scholar
  11. 11.
    O. Perron, Die Lehre von den Kettenbrüchen, Band 1, Teubner, Stuttgart (1954).MATHGoogle Scholar
  12. 12.
    M. M. Pahirya, “Interpolation of functions by continued fractions and branching continued fractions of a special form,” Nauk. Visn. Uzhhorod Univ., Ser. Mat., Issue 1, 72–79 (1994).Google Scholar
  13. 13.
    M. M. Pahirya, “Problem of interpolation of functions by continued fractions,” Nauk. Visn. Uzhhorod Univ., Ser. Mat., Issue 10–11, 77–87 (2005).Google Scholar
  14. 14.
    F. B. Hildebrand, Introduction to Numerical Analysis, Dover, New York (1987).MATHGoogle Scholar
  15. 15.
    M. M. Pahirya, “Some types of interpolation continued fractions,” in: Computer Mathematics. Optimization of Computation, Proc. of the Institute of Cybernetics, Ukrainian National Academy of Sciences, Vol. 1, Kyiv (2001), pp. 328–333.Google Scholar
  16. 16.
    M. M. Pahirya, “Interpolation function of non-Thiele continued fractions,” Comm. Anal. Theory Contin. Fractions, 10, 59–62 (2002).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • M. M. Pahirya
    • 1
  1. 1.Mukachevo State UniversityMukachevoUkraine

Personalised recommendations