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Volume 10, Issue 3
The Dimensions of Spline Spaces and Their Singularity

Xi-Quan Shi

J. Comp. Math., 10 (1992), pp. 224-230.

Published online: 1992-10

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  • Abstract

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.  

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@Article{JCM-10-224, author = {Shi , Xi-Quan}, title = {The Dimensions of Spline Spaces and Their Singularity}, journal = {Journal of Computational Mathematics}, year = {1992}, volume = {10}, number = {3}, pages = {224--230}, abstract = {

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.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9355.html} }
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.  

Shi , Xi-Quan. (1992). The Dimensions of Spline Spaces and Their Singularity. Journal of Computational Mathematics. 10 (3). 224-230. doi:
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