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 - <p style="text-align: justify;">In this paper, &nbsp;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.</p>