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An iterative method for computing multivariate \(C^ 1\) piecewise polynomial interpolants. (English) Zbl 0637.65008
The author presents an iterative method for computing a multivariate C 1 spline interpolant. The idea is to take the piecewise linear interpolant and to compute a perturbation of it which satisfies the desired smoothness conditions. In particular, given a collection of points in \(R^ m\), together with a triangulation of those points, the scheme described requires only the values of the function to be interpolated at the given points. The result is a \(C^ 1\) interpolant whose restriction to each of the triangles in the triangulation is a polynomial of degree n.
Reviewer: A.López-Carmona

MSC:
65D07 Numerical computation using splines
65D05 Numerical interpolation
41A15 Spline approximation
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
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