Convergent Vector and Hermite Subdivision Schemes |
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Authors: | Serge Dubuc Jean-Louis Merrien |
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Institution: | (1) Departement de Mathematiques et de Statistique, C.P. 6128 Succursale Centre-ville, Montreal (Quebec) H3C 3J7, Canada;(2) INSA de Rennes, 20 av. des Buttes de Coesmes, CS 14315, 35043 Rennes cedex, France |
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Abstract: | Hermite subdivision schemes have been studied by Merrien, Dyn, and Levin
and they appear to be very different from subdivision schemes analyzed before since the rules depend on the subdivision level.
As suggested by Dyn and Levin, it is possible to transform the initial scheme into a uniform stationary vector subdivision
scheme which can be handled more easily.With this transformation, the study of convergence of Hermite subdivision schemes
is reduced to that of vector stationary subdivision schemes. We propose a first criterion for C0-convergence for a large class of vector subdivision schemes. This gives a criterion for C1-convergence of Hermite subdivision schemes. It can be noticed that these schemes do not have to be interpolatory. We conclude
by investigating spectral properties of Hermite schemes and other necessary/sufficient conditions of convergence. |
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Keywords: | Subdivision Convergence Hermite interpolation |
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