Skip to main content
SpringerLink
Log in

Barycentric coordinates for Lagrange interpolation over lattices on a simplex

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

Abstract

In this paper, a (d + 1)-pencil lattice on a simplex in \({\mathbb{R}}^d\) is studied. The lattice points are explicitly given in barycentric coordinates. This enables the construction and the efficient evaluation of the Lagrange interpolating polynomial over a lattice on a simplex. Also, the barycentric representation, based on shape parameters, turns out to be appropriate for the lattice extension from a simplex to a simplicial partition.

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. Carnicer, J.M., Gasca, M., Sauer, T.: Interpolation lattices in several variables. Numer. Math. 102(4), 559–581 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chung, K.C., Yao, T.H.: On lattices admitting unique Lagrange interpolation. SIAM J. Numer. Anal. 14(4), 735–743 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  3. Gasca, M., Sauer, T.: Polynomial interpolation in several variables. Adv. Comput. Math. 12(4), 377–410 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. Jaklič, G., Kozak, J., Krajnc, M., Vitrih, V., Žagar, E.: Three-pencil lattices on triangulations. Numer. Algorithms 45(1–4), 49–60 (2007)

    Article  MathSciNet  Google Scholar 

  5. Lai, M.J., Schumaker, L.L.: Spline Functions on Triangulations. Encyclopedia of Mathematics and its Applications. Cambridge University Press (2007)

  6. Lee, S.L., Phillips, G.M.: Construction of lattices for Lagrange interpolation in projective space. Constr. Approx. 7(3), 283–297 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  7. Phillips, G.M.: Interpolation and Approximation by Polynomials. CMS books in Mathematics. Springer, Berlin Heidelberg New York (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FMF, University of Ljubljana, Ljubljana, Slovenia

    Gašper Jaklič, Jernej Kozak & Emil Žagar

  2. IMFM, University of Ljubljana, Ljubljana, Slovenia

    Jernej Kozak, Marjeta Krajnc & Emil Žagar

  3. PINT, University of Primorska, Koper, Slovenia

    Gašper Jaklič & Vito Vitrih

Authors
  1. Gašper Jaklič
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jernej Kozak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marjeta Krajnc
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vito Vitrih
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Emil Žagar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Emil Žagar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jaklič, G., Kozak, J., Krajnc, M. et al. Barycentric coordinates for Lagrange interpolation over lattices on a simplex. Numer Algor 48, 93–104 (2008). https://doi.org/10.1007/s11075-008-9178-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11075-008-9178-7

Keywords

Mathematics Subject Classifications (2000)

Search

Navigation