Skip to main content
SpringerLink
Log in

B-splines from parallelepipeds

  • Published:
Journal d’Analyse Mathématique Aims and scope

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

References

  1. C. de Boor,Splines as linear combinations of B-splines, inApproximation Theory II, G. G. Lorentz, C. K. Chui and L. L. Schumaker (eds.), Academic Press, 1976, pp. 1–47.

  2. C. de Boor and R. DeVore,Approximation by smooth multivariate splines, Trans. Am. Math. Soc.276 (1983), 775–788.

    Article  MATH  Google Scholar 

  3. C. de Boor and K. Höllig,Recurrence relations for multivariate B-splines, Proc. Am. Math. Soc.85 (1982), 397–400.

    Article  MATH  Google Scholar 

  4. C. de Boor and K. Höllig,Bivariate box splines and smooth pp functions on a three-direction mesh, J. Comput. Appl. Math.9 (1983), 13–28.

    Article  MATH  MathSciNet  Google Scholar 

  5. W. Dahmen,On multivariate B-splines, SIAM J. Numer. Anal.17 (1980), 179–191.

    Article  MATH  MathSciNet  Google Scholar 

  6. W. Dahmen,Multivariate B-splines — recurrence relations and linear combinations of truncated powers, inMultivariate Approximation Theory, W. Schempp and K. Zeller (eds.), BirkhÄuser, Basel, 1979, pp. 64–82.

    Google Scholar 

  7. W. Dahmen,Konstruktion mehrdimensionaler B-splines und ihre Anwendungen auf Approximationsprobleme, inNumerische Methoden der Approximationstheorie, Bd. 5, L. Collatz, G. Meinardus and H. Werner (eds.), BirkhÄuser, Basel, 1980, pp. 84–110.

    Google Scholar 

  8. W. Dahmen,Approximation by smooth multivariate splines on non-uniform grids, inQuantitative Approximation, R. DeVore and K. Scherer (eds.), Academic Press, 1980, pp. 99–114.

  9. W. Dahmen and C. A. Micchelli,On limits of multivariate B-splines, MRC TSR #2114, 1980; J. Anal. Math.39 (1981), 256–278.

  10. W. Dahmen and C. A. Micchelli,On the linear independence of multivariate B-splines. I. Triangulation of simploids, SIAM J. Numer. Anal.19 (1982), 993–1012.

    Article  MATH  MathSciNet  Google Scholar 

  11. W. Dahmen and C. A. Micchelli,On the linear independence of multivariate B-splines. II. Complete configurations, Math. Comp., to appear.

  12. P. O. Frederickson,Generalized triangular splines, Mathematics Report 7-71, Lakehead University, 1971.

  13. P. O. Frederickson,Quasi-interpolation, extrapolation, and approximation on the plane, inProc. Manitoba Conference on Numerical Mathematics, Winnipeg, 1971, pp. 169–176.

  14. G. Fix and G. Strang,Fourier analysis of the finite element method in Ritz—Galerkin theory, Stud. Appl. Math.48 (1969), 265–273.

    MATH  MathSciNet  Google Scholar 

  15. T. N. T. Goodman and S. L. Lee,Spline approximation operators of Bernstein-Schoenberg type in one and two variables, J. Approx. Theory33 (1981), 248–263.

    Article  MATH  MathSciNet  Google Scholar 

  16. H. Hakopian,Multivariate divided differences and multivariate interpolation of Lagrange and Hermite type, J. Approx. Theory34 (1982), 286–305.

    Article  MATH  MathSciNet  Google Scholar 

  17. H. Hakopian,Les différences divisées de plusieurs variables et les interpolations multidimensionelles de types lagrangien et hermitien, Comptes Rendus Acad. Sci. Paris292 (1981), 453–456.

    MATH  MathSciNet  Google Scholar 

  18. H. Hakopian,Multivariate divided differences and multivariate interpolation of Lagrange and Hermite type, SIAM J. Numer. Anal.19 (1982), 510–517.

    Article  MATH  MathSciNet  Google Scholar 

  19. K. Höllig,A remark on multivariate B-splines, J. Approx. Theory33 (1981), 119–125.

    Article  MathSciNet  Google Scholar 

  20. K. Höllig,Multivariate Splines, SIAM J. Numer. Anal.19 (1982), 1013–1031.

    Article  MATH  MathSciNet  Google Scholar 

  21. C. A. Micchelli,A constructive approach to Kergin interpolation in R k:multivariate B-splines and Lagrange interpolation, MRC TSR #1895 (1978); Rocky Mountain J. Math.10 (1980), 485–497.

  22. C. A. Micchelli,On a numerically efficient method for computing multivariate B-splines, inMultivariate Approximation Theory, W. Schempp and K. Zeller (eds.), BirkhÄuser, Basel, 1979, pp. 211–248.

    Google Scholar 

  23. M. J. D. Powell,Piecewise quadratic surface fitting for contour plotting, inSoftware for Numerical Mathematics, D. J. Evans (ed.), Academic Press, 1974, pp. 253–271.

  24. M. J. D. Powell and M. A. Sabin,Piecewise quadratic approximations on triangles, ACM Trans. Math. Software3 (1977), 316–325.

    Article  MATH  MathSciNet  Google Scholar 

  25. P. Sablonniere, unpublished notes 1979; part of the material has appeared in reports, e.g., inDe l’existence de spline à support borné sur une triangulation équilatérale du plan, Publication ANO-39, U.E.R. d’I.E.E.A. — Informatique, Université de Lille I, 1981.

  26. I. J. Schoenberg, Letter to Philip J. Davis dated May 31, 1965.

  27. P. Zwart,Multivariate splines with nondegenerate partitions, SIAM J. Numer. Anal.10 (1973), 665–673.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Research Center, University of Wisconsin, 53706, Madison, WI, USA

    C. De Boor & K. Höllig

Authors
  1. C. De Boor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Höllig
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Sponsored by the United States Army under Contract No. DAAG29-80-C-0041.

Supported in part by the National Science Foundation under Grant No. MCS-7927062.

Rights and permissions

Reprints and permissions

About this article

Cite this article

De Boor, C., Höllig, K. B-splines from parallelepipeds. J. Anal. Math. 42, 99–115 (1982). https://doi.org/10.1007/BF02786872

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02786872

Keywords

Search

Navigation