四点插值细分算法的光滑度

Smoothness of 4-Point Interpolatory Subdivision Schemes

将Dyn,Levin,和Gregory关于四点插值细分算法极限曲线的光滑性的结论从细分权值对称的情形推广到权值不对称的情形,并给出了此情形下四点插值细分算法极限曲线具有连续的一阶导数的充分条件和必要条件。同时还利用矩阵的广义特征向量理论,将Dyn等人以及曹沅关于四点插值细分曲线一般不存在二阶导数的证明从权值对称情形推广到权值不对称的情形。

Dyn,Levin and Gregory＇s results on smoothness of 4-point interpolatory subdivision schemes from symmtric mask case to nonsymmetric mask case are generalized.For 4-point interpolatory subdivision schemes with nonsymmetric masks,sufficient conditions and necessary conditions for limit functions to be C1 are given and also proved that limit functions are not twice differentiable in general.