Numerical Algorithms

, Volume 76, Issue 3, pp 709–725 | Cite as

Hermite interpolation with symmetric polynomials

  • Phung Van ManhEmail author
Original Paper


We study the Hermite interpolation problem on the spaces of symmetric bivariate polynomials. We show that the multipoint Berzolari-Radon sets solve the problem. We also give a Newton formula for the interpolation polynomial and use it to prove a continuity property of the interpolation polynomial with respect to the interpolation points.


Polynomial interpolation Hermite interpolation Multipoint berzolari-radon set 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bojanov, B., Hakopian, H., Sahakian, A.: Spline functions and multivariate interpolations. Springer-Verlag (1993)Google Scholar
  2. 2.
    Bos, L.: On certain configurations of points in \(\mathbb {R}^{n}\) which are unisolvent for polynomial interpolation. J. Approx. Theory 64, 271–280 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Bos, L., Calvi, J.-P.: Multipoint Taylor interpolation. Calcolo 45, 35–51 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Bos, L., Calvi, J.-P.: Taylorian points of an algebraic curve and bivariate Hermite interpolation. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 7, 545–577 (2008)zbMATHGoogle Scholar
  5. 5.
    Calvi, J.-P., Phung, V.M.: On the continuity of multivariate Lagrange interpolation at natural lattices. L.M.S. J. Comp. Math. 6, 45–60 (2013)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Calvi, J.-P., Phung, V.M.: Can we define Taylor polynomials on algebraic curve. Ann. Polon. Math. 118, 1–24 (2016)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Carnicer, J.M., Godés, C.: Interpolation with symmetric polynomials. Numer. Algorithms 74, 1–18 (2017)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Gasca, M., Maeztu, J.I.: On Lagrange and Hermite interpolation in \(\mathbb {R}^{k}\). Numer. Math. 39, 1–14 (1982)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Phung, V.M.: On bivariate Hermite interpolation and the limit of certain bivariate Lagrange projectors. Ann. Polon. Math. 115, 1–21 (2015)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Phung, V.M.: Continuity and convergence properties of integral means of Bojanov-Xu interpolation. Preprint (2015)Google Scholar
  11. 11.
    Roman, S.: The formula of Faa di Bruno. Amer. Math. Monthly 87, 805–809 (1980)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsHanoi National University of EducationHanoiVietnam

Personalised recommendations