An algebraic approach to polynomial reproduction of Hermite subdivision schemes
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Publication:6299733
DOI10.1016/J.CAM.2018.08.009arXiv1803.11007WikidataQ129401233 ScholiaQ129401233MaRDI QIDQ6299733
Publication date: 29 March 2018
Abstract: We present an accurate investigation of the algebraic conditions that the symbols of a univariate, binary, Hermite subdivision scheme have to fulfil in order to reproduce polynomials. These conditions are sufficient for the scheme to satisfy the so called spectral condition. The latter requires the existence of particular polynomial eigenvalues of the stationary counterpart of the Hermite scheme. In accordance with the known Hermite schemes, we here consider the case of a Hermite scheme dealing with function values, first and second derivatives. Several examples of application of the proposed algebraic conditions are given in both the primal and the dual situation.
Numerical interpolation (65D05) Interpolation in approximation theory (41A05) Computer-aided design (modeling of curves and surfaces) (65D17)
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