Instability in the dimension of spaces of bivariate piecewise polynomials of degree 2 r and smoothness order r
Instability in the dimension of spaces of bivariate piecewise polynomials of degree 2 r and smoothness order r
复制标题
DOI：
10.1137/0727034
复制
发表时间：
1990-04
影响因子：
2.9
通讯作者：
D. Diener
中科院分区：
文献类型：
--
作者：
D. Diener
研究了一个特殊三角剖分上的二元样条空间。在这个三角剖分上，具有2次和1阶光滑度的样条空间的维数长期以来一直被认为取决于三角剖分的几何形状。这个结果被推广到2 r次光滑阶为r的样条空间。样条空间的维度被证明对$r \geqq 1$的所有值具有类似的几何依赖性。
The spaces of bivariate splines on a particular triangulation are considered. The dimension of the space of splines with degree 2 and with smoothness order 1 on this triangulation has long been known to depend on the geometry of the triangulation. This result is extended to the space of splines of degree $2r$ and smoothness order r. The dimension of the spline space is shown to have a similar dependence on geometry for all values of $r \geqq 1$.