Abstract
The well-known square mesh with both diagonals drawn in is generalized to the m-dimensional mesh Δ m generated by {(v 1, ..., v m ): v i ∈ {−1, 0, 1}, i = 1,...,m}. Sharp necessary and sufficient conditions on data at the vertices of Δ m are given that allow interpolation of the data by m-variate, C 1 piecewise polynomials of degree m + 1. For degree m + 2 and higher, values and normals at the vertices can be stably interpolated and a unit-norm C 2 Lagrange function for each vertex is exhibited.
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Dedicated to the memory of Lothar Collatz
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© 1992 Springer Basel AG
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Neff, A., Peters, J. (1992). C1 Interpolation on Higher-Dimensional Analogues of the 4-Direction Mesh. In: Braess, D., Schumaker, L.L. (eds) Numerical Methods in Approximation Theory, Vol. 9. ISNM 105: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 105. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8619-2_12
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DOI: https://doi.org/10.1007/978-3-0348-8619-2_12
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