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Estimation of the Remainder for the Interpolation Continued C-Fraction

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Ukrainian Mathematical Journal Aims and scope

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

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References

  1. I. P. Havrylyuk and V. L. Makarov, Numerical Methods, Part 1 [in Ukrainian], Vyshcha Shkola, Kyiv (1995).

    Google Scholar 

  2. A. A. Privalov, Theory of Interpolation of Functions [in Russian], Saratov University, Saratov (1990).

    Google Scholar 

  3. G. A. Baker, Jr., and P. Graves-Morris, Padé Approximants, Addison-Wesley, London (1981).

    Google Scholar 

  4. V. Ya. Skorobogat’ko, Theory of Branching Continued Fractions and Its Application in Numerical Mathematics [in Russian], Nauka, Kiev (1983).

    Google Scholar 

  5. J. M. Hoene-Wroński, Introduction à la Philosophie des Mathématiques et Technie de l’Algorithmique, Courcier, Paris (1811).

    Google Scholar 

  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).

  7. T. N. Thiele, Interpolationsprechnung, Commisission von B. G. Teubner, Leipzig (1909).

    Google Scholar 

  8. L. M. Milne-Thomson, The Calculus of Finite Differences, MacMillan, London (1933).

    Google Scholar 

  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).

    MathSciNet  Google Scholar 

  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).

  11. O. Perron, Die Lehre von den Kettenbrüchen, Band 1, Teubner, Stuttgart (1954).

    MATH  Google Scholar 

  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).

  13. M. M. Pahirya, “Problem of interpolation of functions by continued fractions,” Nauk. Visn. Uzhhorod Univ., Ser. Mat., Issue 10–11, 77–87 (2005).

  14. F. B. Hildebrand, Introduction to Numerical Analysis, Dover, New York (1987).

    MATH  Google Scholar 

  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.

  16. M. M. Pahirya, “Interpolation function of non-Thiele continued fractions,” Comm. Anal. Theory Contin. Fractions, 10, 59–62 (2002).

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Mukachevo State University, Mukachevo, Ukraine

    M. M. Pahirya

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  1. M. M. Pahirya
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 6, pp. 806–814, June, 2014.

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Pahirya, M.M. Estimation of the Remainder for the Interpolation Continued C-Fraction. Ukr Math J 66, 905–915 (2014). https://doi.org/10.1007/s11253-014-0980-1

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  • DOI: https://doi.org/10.1007/s11253-014-0980-1

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