1. MMC
  2. All Volumes and Issues
  3. Volume 6, Number 1, 2019
  4. Interpolation integral continued fraction with twofold node

Interpolation integral continued fraction with twofold node

MMC.
2019;
Volume 6, Number 1
: pp. 1-13
https://doi.org/10.23939/mmc2019.01.001
Received: October 15, 2018
Accepted: January 24, 2019

Math. Model. Comput. Vol.6, No.1, pp.1-13 (2019)

Authors:
  1. Ihor Demkiv
  2. I. Ivasiuk
  3. M. Kopach
1
Lviv Polytechnic National University
2
Vasyl Stefanyk Precarpathian National University
3
Vasyl Stefanyk Precarpathian National University

For a functional given on a continual set of nodes on the basis of the previously constructed interpolation integral continued fraction of the Newton type, an interpolant with a $k$-th twofold node has been constructed and investigated. It is proved that the constructed integral continued fraction is an interpolant of the Hermitian type.

Newton type interpolation continued fraction
twofold node of continued fraction
Hermitian type interpolant
  1. Mykhal'chuk B. R. Interpolation of nonlinear functionals by integral continued fractions.  Ukr. Math. J.  51 (3), 406--418 (1999).
  2. Makarov V. L., Khlobystov V. V., Mykhal'chuk B. R.  Interpolational Integral Continued Fractions.  Ukr. Math. J. 55 (4), 576--587 (2003).
  3. Makarov V. L., Demkiv I. I., Mykhal'chuk B. R.  Necessary and sufficient conditions of interpolation functional polynomial existence on continual sets of knots.  Dopov. Nac. akad. nauk Ukr. 7, 7 (2003).
  4. Makarov V. L., Demkiv I. I.  New class of Interpolation integral continued fractions.  Dopov. Nac. akad. nauk Ukr. 11, 17 (2008).
  5. Makarov V. L., Demkiv I. I.  Relation between interpolating integral continued fractions and interpolating branched continued fractions.  J. Math. Sci. 165 (2), 171--180 (2010).
  6. Makarov V. L., Khlobystov V. V., Demkiv I. I.  Hermitian functional polynomials in space $Q[0,1]$.  Dopov. Nac. akad. nauk Ukr.  8, 27 (2007).