Abstract
In this paper we begin to explore a new method of analyzing the regularity of Hermite subdivision schemes that are defined from local polynomial interpolants. The idea of the method is to view the limit of the scheme as the limit of splines formed by these local interpolants rather than as the limit of polygons. We demonstrate the success of the method by obtaining the precise Hölder regularity of the simple, but non-trivial scheme in which the data are uniformly spaced and the refinement rule is defined by quintic interpolation of four values and two derivatives.
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Communicated by Per Lötstedt.
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Floater, M.S., Siwek, B.P. Analysis of Hermite subdivision using piecewise polynomials. Bit Numer Math 53, 397–409 (2013). https://doi.org/10.1007/s10543-012-0418-9
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DOI: https://doi.org/10.1007/s10543-012-0418-9