TY - JOUR T1 - The Dimensions of Spline Spaces and Their Singularity AU - Shi , Xi-Quan JO - Journal of Computational Mathematics VL - 3 SP - 224 EP - 230 PY - 1992 DA - 1992/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9355.html KW - AB -

In this paper, the dimensions of spaces $S^{\mu}_k(\Delta_n)(k\geq 2^n\mu +1)$ are obtained, where $(\Delta_n)$ is a general simplicial partition of a bounded region with piecewise linear boundary. It is also pointed that the singularity of spaces $S^{\mu}_k(\Delta_n)$ can not disappear when $n\geq 3$ no matter how large $k$ is. At the same time, a necessary and sufficient condition that Morgen and Scott's structure is singular is obtained.