On the Approximation of the Derivatives of Spline Quasi-Interpolation in Cubic Spline $S_3^{1,2}(∆_{mn}^{(2)})$
Year: 2014
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 1 : pp. 1–22
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2014.y12035
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 1 : pp. 1–22
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Bivariate splines conformality of smoothing cofactor method nonuniform type-2 triangulation quasi-interpolation modulus of continuity.
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Bivariate Polynomial Interpolation over Nonrectangular Meshes
Qian, Jiang
Zheng, Sujuan
Wang, Fan
Fu, Zhuojia
Numerical Mathematics: Theory, Methods and Applications, Vol. 9 (2016), Iss. 4 P.549
https://doi.org/10.4208/nmtma.2016.y15027 [Citations: 0]