C 1 -Cubic Quasi-Interpolation Splines over a CT Refinement of a Type-1 Triangulation

Haithem Benharzallah, Abdelaziz Mennouni and Domingo Barrera ()
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Haithem Benharzallah: Department of Mathematics, LTM, University of Batna 2, Mostefa Ben Boulaïd, Fesdis, Batna 05078, Algeria
Abdelaziz Mennouni: Department of Mathematics, LTM, University of Batna 2, Mostefa Ben Boulaïd, Fesdis, Batna 05078, Algeria
Domingo Barrera: Department of Applied Mathematics, University of Granada, 18071 Granada, Spain

Mathematics, 2022, vol. 11, issue 1, 1-19

Abstract: C 1 continuous quasi-interpolating splines are constructed over Clough–Tocher refinement of a type-1 triangulation. Their Bernstein–Bézier coefficients are directly defined from the known values of the function to be approximated, so that a set of appropriate basis functions is not required. The resulting quasi-interpolation operators reproduce cubic polynomials. Some numerical tests are given in order to show the performance of the approximation scheme.

Keywords: Bernstein–Bézier coefficients; quasi-interpolation; type-1 triangulation; Clough–Tocher split (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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