Skip to main content
Log in

Integral Newton-Type Polynomials with Continual Nodes

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We construct an integral Newton-type interpolation polynomial with a continual set of nodes. This interpolant is unique and preserves an operator polynomial of the corresponding degree.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. P. M. Prenter, “Lagrange and Hermite interpolation in Banach spaces,” Approxim. Theory, 4, No. 4, 419-432 (1971).

    Google Scholar 

  2. W. A. Porter, “Data interpolation: causality structure and system identification,” Inform. Contr., 29, No. 3, 217-233 (1975).

    Google Scholar 

  3. A. D. Egorov, P. I. Sobolevskii, and L. A. Yanovich, Approximate Methods for the Calculation of Continual Integrals [in Russian], Nauka i Tekhnika, Minsk (1985).

  4. V. L. Makarov and V. V. Khlobystov, “On the general structure of polynomial functional interpolants,” Dokl. Akad. Nauk SSSR, 318, No. 4, 805-808 (1991).

    Google Scholar 

  5. V. L. Makarov and V. V. Khlobystov, “Polynomial interpolation of nonlinear functionals,” Dokl. Akad. Nauk SSSR, 321, 470-473 (1991).

    Google Scholar 

  6. V. L. Makarov and V. V. Khlobystov, “Polynomial interpolation of operators in Hilbert spaces,” Dokl. Akad. Nauk Rossii, 324, No. 4, 742-745 (1992).

    Google Scholar 

  7. V. L. Makarov and V. V. Khlobystov, “Hermite interpolation of operators in Hilbert spaces,” Dokl. Akad. Nauk Rossii, 327, No. 2, 183-186 (1992).

    Google Scholar 

  8. V. L. Makarov and V. V. Khlobystov, “Polynomial interpolation of operators in vector spaces,” Dokl. Akad. Nauk Rossii, 329, No. 2, 135-139 (1993).

    Google Scholar 

  9. V. L. Makarov and V. V. Khlobystov, Foundations of the Theory of Polynomial Operator Interpolation [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1998).

    Google Scholar 

  10. V. L. Makarov, V. V. Khlobystov, and L. A. Yanovich, Interpolation of Operators [in Russian], Naukova Dumka, Kiev (2000).

    Google Scholar 

  11. V. L. Makarov and V. V. Khlobystov, “ Newton-type interpolation formula for nonlinear functionals,” Dokl. Akad. Nauk SSSR, 307, No. 3, 534-537 (1989).

    Google Scholar 

  12. W. A. Porter, “Synthesis of polynomic system,” SIAM J. Math. Anal., 11, No. 2, 308-315 (1980).

    Google Scholar 

  13. K. I. Pupkov, V. I. Kapalin, and A. S. Yushchenko, Functional Series in the Theory of Nonlinear Systems [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  14. V. I. Averbukh and O. G. Smolyanov, “Theory of differentiation in linear topological spaces,” Usp. Mat. Nauk, 22, No. 6, 201-260 (1967).

    Google Scholar 

  15. P. Antosik, J. Mikusi?ski, and R. Sikorski, Theory of Distributions. The Sequential Approach, Elsevier, Amsterdam (1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Makarov, V.L., Khlobystov, V.V., Kashpur, E.F. et al. Integral Newton-Type Polynomials with Continual Nodes. Ukrainian Mathematical Journal 55, 942–955 (2003). https://doi.org/10.1023/B:UKMA.0000010594.60504.08

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:UKMA.0000010594.60504.08

Keywords

Navigation