摘要
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.
基金
The authors wish to express our great appreciation to Prof.Renhong Wang for his valuable suggestions.Also,the authors would like to thank Dr.Chongjun Li and Dr.Chungang Zhu for their help
This work is supported by National Basic Research Program of China(973 Project No.2010CB832702)
R and D Special Fund for Public Welfare Industry(Hydrodynamics,Grant No.201101014)
National Science Funds for Distinguished Young Scholars(Grant No.11125208)
Programme of Introducing Talents of Discipline to Universities(111 project,Grant No.B12032)
This work is supported by the Fundamental Research Funds for the Central Universities,and Hohai University Postdoctoral Science Foundation 2016-412051.
