From Hermite to stationary subdivision schemes in one and several variables |
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Authors: | Jean–Louis Merrien Tomas Sauer |
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Institution: | 1.INSA de Rennes,Rennes Cedex,France;2.Lehrstuhl für Numerische Mathematik,Justus–Liebig–Universit?t Gie?en,Gie?en,Germany |
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Abstract: | Vector and Hermite subdivision schemes both act on vector data, but since the latter one interprets the vectors as function
values and consecutive derivatives they differ by the “renormalization” of the Hermite scheme in any step. In this paper we
give an algebraic factorization method in one and several variables to relate any Hermite subdivision scheme that satisfies
the so–called spectral condition to a vector subdivision scheme. These factorizations are natural extensions of the “zero
at π” condition known for the masks of refinable functions. Moreover, we show how this factorization can be used to investigate
different forms of convergence of the Hermite scheme and why the multivariate situation is conceptionally more intricate than
the univariate one. Finally, we give some examples of such factorizations. |
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