The Dimensions of Spline Spaces and Their Singularity (Journal of Computational Mathematics, 1992)
In this paper, the dimensions of spaces $S^{μ}_k(Δ_n)(k≥ 2^nμ +1)$ are obtained, where $(Δ_n)$ is a general simplicial partition of a bounded region with piecewise linear boundary. It is also pointed that the singularity of spaces $S^{μ}_k(Δ_n)$ can not disappear when $n≥ 3$ 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.