On the norms of the Dubuc-Deslauriers subdivision schemes
نویسندگان
چکیده
Conti et al. (2012, Remark 3.4) conjecture that the norm of the interpolatory 2n-point Dubuc–Deslauriers subdivision scheme is bounded from above by 4 for any n ∈ N. We disprove their conjecture by showing that the norm grows logarithmically in n and therefore diverges as n increases.
منابع مشابه
Interpolatory blending net subdivision schemes of Dubuc-Deslauriers type
Net subdivision schemes recursively refine nets of univariate continuous functions defined on the lines of planar grids, and generate as limits bivariate continuous functions. In this paper a family of interpolatory net subdivision schemes related to the family of Dubuc-Deslauriers interpolatory subdivision schemes is constructed and analyzed. The construction is based on Gordon blending interp...
متن کاملParametric Families of Hermite Subdivision Schemes in Dimension 1
We introduce a class of stationary 1-D interpolating subdivision schemes, denoted by Hermite(m, L, k), which classifies all stationary Lagrange or Hermite interpolating subdivision schemes with prescribed multiplicity, support and polynomial reproduction property: Given m > 0, L > 0 and 0 ≤ k ≤ 2mL − 1, Hermite(m, L, k) is a family parametrized by m2L− m(k +1)/2 (in the symmetric case) or 2m2L−...
متن کاملInterpolatory Subdivision and Wavelets on an Interval
We consider a method of adapting Dubuc-Deslauriers sudivision, which is de ̄ned for bi-in ̄nite sequences, to accommodate sequences of ̄nite length. After deriving certain useful properties of the Dubuc-Deslauriers re ̄nable function on R, we de ̄ne a multi-scale ̄nite sequence of functions on a bounded interval, which are then proved to be re ̄nable. Using this fact, the resulting adapted interpolato...
متن کاملSymbols and exact regularity of symmetric pseudo-splines of any arity
Pseudo-splines form a family of subdivision schemes that provide a natural blend between interpolating schemes and approximating schemes, including the Dubuc-Deslauriers schemes and B-spline schemes. Using a generating function approach, we derive expressions for the symbols of the symmetric m-ary pseudo-spline subdivision schemes. We show that their masks have positive Fourier transform, makin...
متن کاملStationary subdivision schemes reproducing polynomials
A new class of subdivision schemes is presented. Each scheme in this class reproduces polynomials up to a certain degree. We find that these schemes extend and unify not only the well-known Deslauriers–Dubuc interpolatory scheme but the quadratic and cubic B-spline schemes. This paper analyze their convergence, smoothness and accuracy. It is proved that the proposed schemes provide at least the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Computer Aided Geometric Design
دوره 30 شماره
صفحات -
تاریخ انتشار 2013