A NEW PROOF OF THE SMOOTHNESS OF 4-POINT DESLAURIERS-DUBUC SCHEME

Abstract

Abstract. It is well-known that the smoothness of 4-point interpolatory Deslauriers-Dubuc(DD) subdivision scheme is C 1. N. Dyn[3] proved that 4-point interpolatory subdivision scheme is C 1 by means of eigenanalysis. In this paper we take advantage of Laurent polynomial method to get the same result, and give new way of strict proof on Laurent polynomial method.