BIT Numerical Mathematics

, Volume 54, Issue 4, pp 1099–1118 | Cite as

Cubic spline quasi-interpolants on Powell–Sabin partitions



By using the polarization identity, we propose a family of quasi-interpolants based on bivariate \({\fancyscript{C}}^1\) cubic super splines defined on triangulations with a Powell–Sabin refinement. Their spline coefficients only depend on a set of local function values. The quasi-interpolants reproduce cubic polynomials and have an optimal approximation order.


Super spline Powell–Sabin splines Normalized B-splines Blossoms Polarization identity Quasi-interpolation 

Mathematics Subject Classification (2010)

41A15 65D05 65D17 



The authors thank the referees for the useful corrections and comments which improved the presentation of the paper.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Faculty of Science and Technology, University Hassan FirstSettatMorocco
  2. 2.Faculty of Science, University Mohammed FirstOujdaMorocco

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