TY - JOUR
T1 - On the Approximation of the Derivatives of Spline Quasi-Interpolation in Cubic Spline $S_3^{1,2}(∆_{mn}^{(2)})$
AU - Jiang Qian & Fan Wang
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 1
EP - 22
PY - 2014
DA - 2014/07
SN - 7
DO - http://doi.org/10.4208/nmtma.2014.y12035
UR - https://global-sci.org/intro/article_detail/nmtma/5863.html
KW - Bivariate splines, conformality of smoothing cofactor method, nonuniform type-2 triangulation, quasi-interpolation, modulus of continuity.
AB - <p style="text-align: justify;">In this paper, based on the basis composed of two sets of splines with distinct local supports, cubic
spline quasi-interpolating operators are reviewed on nonuniform type-2 triangulation. The variation diminishing operator is defined by discrete linear functionals based on a fixed number of triangular mesh-points, which can reproduce any polynomial of nearly best degrees. And by means of the modulus of continuity, the estimation of the operator approximating a real sufficiently smooth function is reviewed as well. Moreover, the derivatives of the nearly optimal variation diminishing operator can approximate that of the real sufficiently smooth function uniformly over quasi-uniform type-2 triangulation. And then the convergence results are worked out.</p>