Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Multivariate convexity preserving interpolation by smooth functions

  • Published:
Advances in Computational Mathematics Aims and scope Submit manuscript

Abstract

A set of multivariate data is called strictly convex if there exists a strictly convex interpolant to these data. In this paper we characterize strict convexity of Lagrange and Hermite multivariate data by a simple property and show that for strict convex data and given smoothness requirements there exists a smooth strictly convex interpolant. We also show how to construct a multivariate convex smooth interpolant to scattered data.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. J.M. Carnicer and W. Dahmen, Convexity preserving interpolation and Powell-Sabin elements, Comp. Aided Geom. Design 9 (1992) 279–289.

    Article  MATH  MathSciNet  Google Scholar 

  2. J.M. Carnicer and W. Dahmen, Characterization of local strict convexity preserving interpolation methods by C1 functions, J. Approx. Theory, to appear.

  3. W. Dahmen and C.A. Micchelli, Convexity of multivariate Bernstein polynomials and box spline surfaces, Studia Sci. Math. Hung. 23 (1988) 265–287.

    MATH  MathSciNet  Google Scholar 

  4. M. Neamtu, A contribution to the theory and practice of multivariate splines, Ph.D. Thesis, University of Twente, the Netherlands (1991).

    Google Scholar 

  5. T. Lyche, A recurrence relation for Chebyshevian B-splines, Constr. Approx. 1 (1985) 155–173.

    Article  MATH  MathSciNet  Google Scholar 

  6. T. Lyche, Discrete B-splines and conversion problems, in:Computation of Curves and Surfaces, eds. W. Dahmen, M. Gasca and C. Micchelli, (Kluwer, Dordrecht, 1990) pp. 117–134.

    Google Scholar 

  7. T. Lyche and L.L. Schumaker, L-spline wavelets, in:Wavelets: Theory, Algorithms, and Applications, eds. C. Chui, L. Montefusco and L. Puccio (Academic Press, New York, 1994) pp. 197–212.

    Google Scholar 

  8. T. Lyche and R. Winther, A stable recurrence relation for trigonometric B-splines, J. Approx. Theory 25 (1979) 266–279.

    Article  MATH  MathSciNet  Google Scholar 

  9. I.J. Schoenberg, On trigonometric spline interpolation, J. Math. Mech. 13 (1964) 795–825.

    MATH  MathSciNet  Google Scholar 

  10. L.L. Schumaker,Spline Functions: Basic Theory (Interscience New York, 1991; reprinted by Krieger, Malabar, Florida, 1993).

    Google Scholar 

  11. L.L. Schumaker, On recursions for generalized splines, J. Approx. Theory 36 (1982) 16–31.

    Article  MATH  MathSciNet  Google Scholar 

  12. L.L. Schumaker, On hyperbolic splines, J. Approx. Theory 38 (1983) 144–166.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad de Zaragoza, E-50009, Zaragoza, Spain

    J. M. Carnicer

Authors
  1. J. M. Carnicer
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by T.N.T. Goodman

Partially supported by DGICYT PS93-0310 and by the EC project CHRX-CT94-0522.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carnicer, J.M. Multivariate convexity preserving interpolation by smooth functions. Adv Comput Math 3, 395–404 (1995). https://doi.org/10.1007/BF02432005

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02432005

Subject classification

Search

Navigation