Skip to main content
SpringerLink
Log in

Construction of lattices for lagrange interpolation in projective space

  • Published:
Constructive Approximation Aims and scope

Abstract

In this article we construct a lattice of points which lie onk+1 pencils of hyperplanes in the projectivek-space, where, with a suitable choice of coordinate system, simple equations of the hyperplanes are obtained. This enables us to construct an interpolation formula on the projectivek-space from which interpolating polynomials on a general class of lattices in the Euclideank-space are obtained via a projective transformation.

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. W. Böhm, G. Farin, J. Kahman (1984):A survey of curve and surface methods in CAGD. Comput. Aided Geom. Design,1:1–60.

    Google Scholar 

  2. G. Z. Chang, P. J. Davis (1984):The convexity of Bernstein polynomials over triangles. J. Approx. Theory,40:11–28.

    Google Scholar 

  3. C. K.Chul, M. J.Lai (preprint):Vandermonde determinants and Lagrange interpolation in Rs.

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

    Google Scholar 

  5. P. G. Ciarlet, P. A. Raviart (1972):General Lagrange and Hermite interpolation in Rn with applications to finite element methods. Arch. Rational Mech. Anal.,46:177–199.

    Google Scholar 

  6. M. Gasca, E. Lebrón (1987):On Aitken-Neville formulae for several variables. In: Numerical Approximation of Partial Differential Equations (E. L. Oritz, ed.). Amsterdam: Elsier, pp. 133–140.

    Google Scholar 

  7. M. Gasca, J. I. Maetzu (1982):On Lagrange and Hermite interpolation in Rk. Numer. Math.,39:1–14.

    Google Scholar 

  8. M. Gasca, V. Ramirez (1984):Interpolation systems in Rk. J. Approx. Theory,42:36–51.

    Google Scholar 

  9. S. L. Lee, G. M. Phillips (1988):Polynomial interpolation at points of a geometric mesh on a triangle. Proc. Roy. Soc. Edinburgh Sect. A,108:75–87.

    Google Scholar 

  10. A. R. Mitchell, G. M. Phillips (1972):Construction of basis functions in the finite element method. BIT,12:81–89.

    Google Scholar 

  11. R. A. Nicolaides (1972):On a class of finite elements generated by Lagrange interpolation. SIAM J. Numer. Analy.,9:435–445.

    Google Scholar 

  12. H. Thacher, E. Milne (1960):Interpolation in several variables. J. Soc. Indust. Appl. Math.,8:33–42.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, 0511, Singapore

    S. L. Lee

  2. The Mathematical Institute, University of St. Andrews, St Andrews, KY16 9SS, Scotland

    G. M. Phillips

Authors
  1. S. L. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. M. Phillips
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Carl de Boor.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, S.L., Phillips, G.M. Construction of lattices for lagrange interpolation in projective space. Constr. Approx 7, 283–297 (1991). https://doi.org/10.1007/BF01888158

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01888158

AMS classification

Key words and phrases

Search

Navigation