Volume 5, Issue 4
The Bases of the Non-Uniform Cubic Spline Space $S_{3}^{1,2}(\Delta_{mn}^{(2)})$

Numer. Math. Theor. Meth. Appl., 5 (2012), pp. 635-652.

Published online: 2012-05

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• Abstract

In this paper,  the dimension of the nonuniform bivariate spline space $S_{3}^{1,2}(\Delta_{mn}^{(2)})$ is discussed based on the theory of multivariate spline space. Moreover, by means of the Conformality of Smoothing Cofactor Method, the basis of $S_{3}^{1,2}(\Delta_{mn}^{(2)})$composed of two sets of splines are worked out in the form of the values at ten domain points in each triangular cell, both of which possess distinct local supports. Furthermore, the explicit coefficients in terms of B-net are obtained for the two sets of splines respectively.

• Keywords

Bivariate spline, conformality of smoothing cofactor method, B-net nonuniform type-2 triangulation.

65D07

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@Article{NMTMA-5-635, author = {}, title = {The Bases of the Non-Uniform Cubic Spline Space $S_{3}^{1,2}(\Delta_{mn}^{(2)})$}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2012}, volume = {5}, number = {4}, pages = {635--652}, abstract = {

In this paper,  the dimension of the nonuniform bivariate spline space $S_{3}^{1,2}(\Delta_{mn}^{(2)})$ is discussed based on the theory of multivariate spline space. Moreover, by means of the Conformality of Smoothing Cofactor Method, the basis of $S_{3}^{1,2}(\Delta_{mn}^{(2)})$composed of two sets of splines are worked out in the form of the values at ten domain points in each triangular cell, both of which possess distinct local supports. Furthermore, the explicit coefficients in terms of B-net are obtained for the two sets of splines respectively.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2012.m10053}, url = {http://global-sci.org/intro/article_detail/nmtma/5953.html} }
TY - JOUR T1 - The Bases of the Non-Uniform Cubic Spline Space $S_{3}^{1,2}(\Delta_{mn}^{(2)})$ JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 635 EP - 652 PY - 2012 DA - 2012/05 SN - 5 DO - http://doi.org/10.4208/nmtma.2012.m10053 UR - https://global-sci.org/intro/article_detail/nmtma/5953.html KW - Bivariate spline, conformality of smoothing cofactor method, B-net KW - nonuniform type-2 triangulation. AB -

In this paper,  the dimension of the nonuniform bivariate spline space $S_{3}^{1,2}(\Delta_{mn}^{(2)})$ is discussed based on the theory of multivariate spline space. Moreover, by means of the Conformality of Smoothing Cofactor Method, the basis of $S_{3}^{1,2}(\Delta_{mn}^{(2)})$composed of two sets of splines are worked out in the form of the values at ten domain points in each triangular cell, both of which possess distinct local supports. Furthermore, the explicit coefficients in terms of B-net are obtained for the two sets of splines respectively.

Jiang Qian, Renhong Wang & Chongjun Li. (2020). The Bases of the Non-Uniform Cubic Spline Space $S_{3}^{1,2}(\Delta_{mn}^{(2)})$. Numerical Mathematics: Theory, Methods and Applications. 5 (4). 635-652. doi:10.4208/nmtma.2012.m10053
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