From symmetric subdivision masks of Hurwitz type to interpolatory subdivision masks (Q732092)

The authors present a general strategy to deduce a family of interpolatory masks from a symmetric Hurwitz non-interpolatory one. This leads back to a polynomial equation involving the symbol of the non-interpolatory subdivision scheme. The solution of the polynomial equation proposed by the authors is suitable for symmetric Hurwitz subdivision symbols. It is observed that a combination of Dubuc-Deslauriers-masks, also based on a polynomial equation solution, which is less general, has been recently studied in [\textit{J. de Villiers} and \textit{K. Hunter}, East J. Approx. Theory 12, No.~2, 151--188 (2006)].