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aequationes mathematicae

, Volume 42, Issue 1, pp 123–136 | Cite as

Identities for piecewise polynomial spaces determined by connection matrices

  • Phillip J. Barry
  • Nira Dyn
  • Ronald N. Goldman
  • Charles A. Micchelli
Research Papers

Summary

TwoB-spline results — Marsden's identity and the de Boor-Fix dual functionals — are extended to geometrically continuous curves determined by connection matrices.

AMS (1980) subject classifications

Primary 41A15 Secondary 65D07 

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References

  1. [DM]
    Dyn, N. andMicchelli, C.,Piecewise polynomial spaces and geometric continuity of curves, Num. Math.54 (1988), 319–337.CrossRefGoogle Scholar
  2. [DEM]
    Dyn, N., Edelman, A. andMicchelli, C.,On locally supported basis functions for the representation of geometrically continuous curves, Analyses7 (1987), 313–341.Google Scholar
  3. [dBF]
    de Boor, C. andFix, G.,Spline interpolation by quasi-interpolants, J. Approx. Theory8 (1973), 19–45.CrossRefGoogle Scholar
  4. [CS]
    Curry, H. B. andSchoenberg, I. J.,On Pòlya frequency functions IV: The fundamental spline functions and their limits, J. Analyse Math.17 (1966), 71–107.Google Scholar
  5. [M]
    Marsden, M. J.,An identity for spline functions with applications to variation-diminishing spline approximation, J. Approx. Theory3 (1970), 7–49.CrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag 1991

Authors and Affiliations

  • Phillip J. Barry
    • 1
  • Nira Dyn
    • 1
  • Ronald N. Goldman
    • 1
  • Charles A. Micchelli
    • 1
  1. 1.Computer Science Dept.Univ. of MinnesotaMinneapolisUSA

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