Skip to main content
SpringerLink
Log in

Interpolation with symmetric polynomials

  • Original Paper
  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

The Lagrange interpolation problem on spaces of symmetric bivariate polynomials is considered to reduce the interpolation problem to problems of approximately half dimension. The Berzolari-Radon construction is adapted to these kinds of problems by considering nodes placed on symmetric lines or symmetric pairs of lines. A Newton formula for the symmetric interpolant using the Berzolari-Radon construction is proposed.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Berzolari, L.: Sulla determinazione di una curva o di una superficie algebrica e su algune questioni di postulazione. Lomb. Ist. Rend. 47, 556–564 (1914)

    MATH  Google Scholar 

  2. Bojanov, B., Xu, Y.: On polynomial interpolation of two variables. J. Approx. Theory 120, 267–282 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Carnicer, J.M., Godés, C.: Interpolation on the disk. Numer. Algorithms 66, 1–16 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  4. Carnicer, J.M., Godés, C.: A Newton formula for generalized Berzolari-Radon sets. Adv. Comput. Math. 41, 373–386 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chung, K.C., Yao, T.H.: On lattices admitting unique Lagrange interpolations. SIAM J. Numer. Anal. 14, 735–743 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gasca, M., Maeztu, J.I.: On Lagrange and Hermite interpolation in R k. Numer. Math. 39, 1–14 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gasca, M., Ramírez, V.: Interpolation systems in R k. J. Approx. Theory 42, 36–51 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kincaid, D., Cheney, E.W.: Numerical analysis: mathematics of scientific computing. Brooks/Cole Publishing Company, Pacific Grove (1990)

    MATH  Google Scholar 

  9. Li, H., Sun, J., Xu, Y.: Discrete Fourier analysis, cubature and interpolation on a hexagon and a triangle. SIAM J. Numer. Anal. 46, 1653–1681 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Li, H., Xu, Y.: Discrete Fourier analysys on a dodecahedron and a tetrahedron. Math. Comput. 78, 999–1029 (2009)

    Article  MATH  Google Scholar 

  11. Micchelli, C. A.: Algebraic aspects of interpolation. In: de Boor, C. (ed.) Approximation Theory, Proceedings of Symposia in Applied Mathematics 36, pp. 81–102. AMS (1986)

  12. Radon, J.: Zur mechanischen kubatur. Monatsh. Math. 52, 286–300 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  13. Rafayelyan, L.: Poised nodes set constructions on algebraic curves. East J. Approx. 17, 285–298 (2011)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemática Aplicada/IUMA, Universidad de Zaragoza, Pedro Cerbuna 12, 50009, Zaragoza, Spain

    J. M. Carnicer

  2. Departamento de Matemática Aplicada, Universidad de Zaragoza, Carretera de Cuarte s/n, 22071, Huesca, Spain

    C. Godés

Authors
  1. J. M. Carnicer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Godés
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. M. Carnicer.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Carnicer, J.M., Godés, C. Interpolation with symmetric polynomials. Numer Algor 74, 1–18 (2017). https://doi.org/10.1007/s11075-016-0135-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11075-016-0135-6

Keywords

Mathematics Subject Classification (2010)

Search

Navigation