Abstract
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.
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The authors thank the referees for the useful corrections and comments which improved the presentation of the paper.
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Communicated by Tom Lyche.
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Lamnii, A., Lamnii, M. & Mraoui, H. Cubic spline quasi-interpolants on Powell–Sabin partitions. Bit Numer Math 54, 1099–1118 (2014). https://doi.org/10.1007/s10543-014-0489-x
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DOI: https://doi.org/10.1007/s10543-014-0489-x
Keywords
- Super spline
- Powell–Sabin splines
- Normalized B-splines
- Blossoms
- Polarization identity
- Quasi-interpolation