拟α-伪样条及其性质

Quasi-α-pseudo spline and its properties

通过增加参数ω,本文给出了一类新面具,即拟α-伪样条.当ω=0时,拟0-伪样条就是伪样条,拟1/2-伪样条就是对偶伪样条.对特殊的ω≠0,本文给出了拟α-伪样条的稳定性、正则性、渐近分析和逼近阶等性质.相关结果表明拟α-伪样条具有与伪样条以及对偶伪样条类似的性质.同时,结果表明只要支撑区间稍长时,加细函数将具有更好的光滑性.

With a tension parameter ω,we,in this paper,introduce a new family of masks,namely quasi-α-pseudo splines.When ω = 0,quasi-α-pseudo splines is the pseudo splines for α = 0 and the dual-pseudo splinesfor α = 1/2.For special ω ≠ 0,we present basics of quasi-α-pseudo splines which include the stability,regularity,asymptotical analysis and approximation order.These results show that the properties of quasi-α-pseudo splinesare similar to the ones of pseudo splines or dual pseudo splines.However,we can get better smoothness of therefinable functions at the expense of slightly larger support.