一类单周期的S_3~1(△_(mn)^((2)))插值

A Certain Periodic Interpolating Spline of S_3~1(△_(mn)^((2)))

样条函数在 CAGD 上有着广泛的应用。本文继续[1]、[2]的工作,主要讨论了平面矩形区域在Ⅱ型三角剖分下的一类单周期二元三次插值样条的存在性和唯一性。给出了单周期样条空间的维数,并着重讨论了单周期样条插值的逼近度。

Let △_(mn)^(2)be a type Ⅱ triangulations of a rectangle D,~≈S_3~1(△_(mn)^(2) be a periodic spline space as shown as(1.2),in this paper,our main re- sults are that.①the existence and uniqueness of a interpolating spline s∈~≈S_3~1(△_(mn)^(2))under satisfying interpolatory conditions(3.1)be discussed, ②the dim ~≈S_3~1(△_(mn)^(2))be given,and③,the approximation degree be obtai- ned as(3.2).