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Volume 22, Issue 6
The Structural Characterization and Locally Supported Bases for Bivariate Super Splines

Zhiqiang Xu & Renhong Wang

J. Comp. Math., 22 (2004), pp. 807-816.

Published online: 2004-12

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  • Abstract

Super splines are bivariate splines defined on triangulations, where the smoothness enforced at the vertices is larger than the smoothness enforced across the edges. In this paper, the smoothness conditions and conformality conditions for super splines are presented. Three locally supported super splines on type-1 triangulation are presented. Moreover, the criteria to select local bases are also given. By using local supported super spline function, a variation-diminishing operator is built. The approximation properties of the operator are also presented.

  • Keywords

Spline, Local bases, Super spline.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-22-807, author = {Xu , Zhiqiang and Wang , Renhong}, title = {The Structural Characterization and Locally Supported Bases for Bivariate Super Splines}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {6}, pages = {807--816}, abstract = {

Super splines are bivariate splines defined on triangulations, where the smoothness enforced at the vertices is larger than the smoothness enforced across the edges. In this paper, the smoothness conditions and conformality conditions for super splines are presented. Three locally supported super splines on type-1 triangulation are presented. Moreover, the criteria to select local bases are also given. By using local supported super spline function, a variation-diminishing operator is built. The approximation properties of the operator are also presented.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8869.html} }
TY - JOUR T1 - The Structural Characterization and Locally Supported Bases for Bivariate Super Splines AU - Xu , Zhiqiang AU - Wang , Renhong JO - Journal of Computational Mathematics VL - 6 SP - 807 EP - 816 PY - 2004 DA - 2004/12 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8869.html KW - Spline, Local bases, Super spline. AB -

Super splines are bivariate splines defined on triangulations, where the smoothness enforced at the vertices is larger than the smoothness enforced across the edges. In this paper, the smoothness conditions and conformality conditions for super splines are presented. Three locally supported super splines on type-1 triangulation are presented. Moreover, the criteria to select local bases are also given. By using local supported super spline function, a variation-diminishing operator is built. The approximation properties of the operator are also presented.

Xu , Zhiqiang and Wang , Renhong. (2004). The Structural Characterization and Locally Supported Bases for Bivariate Super Splines. Journal of Computational Mathematics. 22 (6). 807-816. doi:
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