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A bivariate $$C^ 2$$ Clough-Tocher scheme. (English) Zbl 0597.65005
Let $${\mathcal D}$$ be a two-dimensional domain that has been triangulated. Using the technique of his earlier paper [ibid. 1, 169-181 (1984; Zbl 0566.65003)] the author constructs a bivariate $${\mathcal C}^ 2$$-interpolant on $${\mathcal D}$$ that requires $${\mathcal C}^ 2$$ data at the scattered points. The scheme is local and has cubic precision.
Reviewer: V.V.Vasil’ev

##### MSC:
 65D05 Numerical interpolation 41A05 Interpolation in approximation theory 41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
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##### References:
 [1] Alfeld, P., A trivariate clough-tocher scheme for tetrahedral data, Computer aided geometric design, 1, 169-181, (1984) · Zbl 0566.65003 [2] Alfeld, P., Multivariate scattered data derivative generation by functional minimization, (1984), submitted for publication [3] Alfeld, P., A bivariate C2 clough-tocher scheme, (), January 1984 · Zbl 0597.65005 [4] Alfeld, P.; Harris, B., MICROSCOPE: A software system for multivariate analysis, (1984), submitted for publication [5] Barnhill, R.E.; Farin, G., C1 quintic interpolation over triangles: two explicit representations, Int. J. for num. meth. in eng., 17, 1763-1778, (1981) · Zbl 0477.65009 [6] Beebe, N.H.F., A User’s guide to PLOT79, (1980), Department of Physics and Chemistry, University of Utah Salt Lake City, UT 84112 [7] Farin, G., Bézier polynomials over triangles and the construction of piecewise Cr polynomials, () [8] Gregory, J.A., Error bounds for linear interpolation on triangles, (), 163-170 [9] Hearn, A.C., (), version 3.0 [10] Ženišek, A., Interpolation polynomials on the triangle, Numer. math., 15, 283-296, (1970) · Zbl 0216.38901
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