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 operat...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.展开更多
In this paper,the dimension of the nonuniform bivariate spline space S_(3)^(1,2)(Δ_(mn)^((2))is discussed based on the theory of multivariate spline space.Moreover,by means of the Conformality of Smoothing Cofactor M...In this paper,the dimension of the nonuniform bivariate spline space S_(3)^(1,2)(Δ_(mn)^((2))is discussed based on the theory of multivariate spline space.Moreover,by means of the Conformality of Smoothing Cofactor Method,the basis ofS_(3)^(1,2)(Δ_(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.展开更多
In this paper,matrix representations of the best spline quasi-interpolating operator over triangular sub-domains in S_(2)^(1)(△_(mn)^(2),and coefficients of splines in terms of B-net are calculated firstly.Moreover,b...In this paper,matrix representations of the best spline quasi-interpolating operator over triangular sub-domains in S_(2)^(1)(△_(mn)^(2),and coefficients of splines in terms of B-net are calculated firstly.Moreover,by means of coefficients in terms of B-net,computation of bivariate numerical cubature over triangular sub-domains with respect to variables x and y is transferred into summation of coefficients of splines in terms of B-net.Thus concise bivariate cubature formulas are constructed over rectangular sub-domain.Furthermore,by means of module of continuity and max-norms,error estimates for cubature formulas are derived over both sub-domains and the domain.展开更多
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 helpThis work is supported by National Basic Research Program of China(973 Project No.2010CB832702)+3 种基金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.
文摘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supported by the National Natural Science Foundation of China(Nos.U0935004,11071031,11001037,10801024)the Fundamental Research Funds for the Central Universities(DUT10ZD112,DUT10JS02).
文摘In this paper,the dimension of the nonuniform bivariate spline space S_(3)^(1,2)(Δ_(mn)^((2))is discussed based on the theory of multivariate spline space.Moreover,by means of the Conformality of Smoothing Cofactor Method,the basis ofS_(3)^(1,2)(Δ_(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.
基金This work was supported by the Fundamental Research Funds for the Central Universities of Hohai University(Grant No.2019B19414,2019B44914)the Natural Science Foundation of Jiangsu Province for the Youth(Grant No.BK20160853)+2 种基金Key Laboratory of Ministry of Education for Coastal Disaster and Protection,Hohai University(Grant No.202011)the National Natural Science Foundation of China(Grant No.11601151)the National Science Foundation of Zhejiang Province(Grant No.LY19A010003).
文摘In this paper,matrix representations of the best spline quasi-interpolating operator over triangular sub-domains in S_(2)^(1)(△_(mn)^(2),and coefficients of splines in terms of B-net are calculated firstly.Moreover,by means of coefficients in terms of B-net,computation of bivariate numerical cubature over triangular sub-domains with respect to variables x and y is transferred into summation of coefficients of splines in terms of B-net.Thus concise bivariate cubature formulas are constructed over rectangular sub-domain.Furthermore,by means of module of continuity and max-norms,error estimates for cubature formulas are derived over both sub-domains and the domain.
