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On the Approximation of the Derivatives of Spline Quasi-Interpolation in Cubic Spline Space

Published online by Cambridge University Press:  28 May 2015

Jiang Qian  and
Fan Wang
Jiang Qian*
Affiliation:
College of Sciences, Hohai University, Nanjing 210098, China Center for Numerical Simulation Software in Engineering and Sciences, Department of Engineering Mechanics, Hohai University, Nanjing 210098, China
Fan Wang
Affiliation:
College of Engineering, Nanjing Agricultural University, Nanjing 210031, China
*
Corresponding author.Email address:qianjianghhu@sina.com
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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.

Keywords

65D0741A25Bivariate splinesconformality of smoothing cofactor methodnonuniform type-2 triangulationquasi-interpolationmodulus of continuity
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 1 , February 2014 , pp. 1 - 22
Copyright
Copyright © Global Science Press Limited 2014

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