Smoothness equivalence properties of univariate subdivision schemes and their projection analogues

نویسنده

  • Philipp Grohs
چکیده

We study the following modification of a linear subdivision scheme S: Let M be a surface embedded in Euclidean space, and P a smooth projection mapping onto M . Then the P -projection analogue of S is defined as T := P ◦ S. As it turns out, the smoothness of the scheme T is always at least as high as the smoothness of the underlying scheme S or the smoothness of P minus 1, whichever is lower. To prove this we use the method of proximity as introduced by Wallner et. al. [10, 9]. While smoothness equivalence results are already available for interpolatory schemes S, this is the first result that confirms smoothness equivalence properties of arbitrary order for general non-interpolatory schemes.

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عنوان ژورنال:
  • Numerische Mathematik

دوره 113  شماره 

صفحات  -

تاریخ انتشار 2009