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Article Dans Une Revue Numerische Mathematik Année : 2019

Generalized Taylor operators, polynomial chains, and Hermite subdivision schemes

Résumé

Hermite subdivision schemes act on vector valued data that is not only considered as functions values in R^r , but as consecutive derivatives, which leads to a mild form of level dependence of the scheme. Previously, we have proved that a property called spectral condition or sum rule implies a factorization in terms of a generalized difference operator that gives rise to a " difference scheme " whose contractivity governs the convergence of the scheme. But many convergent Hermite schemes, for example, those based on cardinal splines, do not satisfy the spectral condition. In this paper, we generalize the property in a way that preserves all the above advantages: the associated factorizations and convergence theory. Based on these results, we can include the case of cardinal splines and also enables us to construct new types of convergent Hermite subdivision schemes.
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Dates et versions

hal-01731590 , version 1 (14-03-2018)
hal-01731590 , version 2 (15-08-2018)

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Jean-Louis Merrien, Tomas Sauer. Generalized Taylor operators, polynomial chains, and Hermite subdivision schemes. Numerische Mathematik, 2019, 142 (1), pp.167-203. ⟨10.1007/s00211-018-0996-9⟩. ⟨hal-01731590v2⟩
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