Abstract
This paper studies the properties of a nonstationary divided difference vector subdivision scheme S B k derived from a stationary vector subdivision scheme SA. We show that a necessary condition for SA to be C1 (i.e., its linear polynomial reproduction property) implies the existence of a difference scheme derived from S B k. This condition turns out to be a necessary condition for the subdivision scheme S B k to be convergent.
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Charina, M., Conti, C. (2003). On Properties of Nonstationary Divided Difference Vector Subdivision Schemes. In: Haussmann, W., Jetter, K., Reimer, M., Stöckler, J. (eds) Modern Developments in Multivariate Approximation. International Series of Numerical Mathematics, vol 145. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8067-1_3
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DOI: https://doi.org/10.1007/978-3-0348-8067-1_3
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