In this paper, we consider the global error bound for the generalized complementarity problem (GCP) with analytic functions. Based on the new technique, we establish computable global error bound under milder conditio...In this paper, we consider the global error bound for the generalized complementarity problem (GCP) with analytic functions. Based on the new technique, we establish computable global error bound under milder conditions, which refines the previously known results.展开更多
In this paper,the King’s type modification of(p,q)-Bleimann-Butzer and Hahn operators is defined.Some results based on Korovkin’s approximation theorem for these new operators are studied.With the help of modulus of...In this paper,the King’s type modification of(p,q)-Bleimann-Butzer and Hahn operators is defined.Some results based on Korovkin’s approximation theorem for these new operators are studied.With the help of modulus of continuity and the Lipschitz type maximal functions,the rate of convergence for these new operators are obtained.It is shown that the King’s type modification have better rate of convergence,flexibility than classical(p,q)-BBH operators on some subintervals.Further,for comparisons of the operators,we presented some graphical examples and the error estimation in the form of tables through MATLAB(R2015a)展开更多
The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of orderα.Applying the Korovkin theorem,we arrive at the convergence of the operator with the...The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of orderα.Applying the Korovkin theorem,we arrive at the convergence of the operator with the aid of moments and central moments.We determine the rate of convergence of the operator using several tools such as K-functional,modulus of continuity,second modulus of continuity.We also give a type of Voronovskaya theorem for estimating error.Moreover,we investigate some results about convergence properties of the operator in a weighted space.Finally,we give numerical examples to support our theorems by using the Maple.展开更多
As an intrinsic measure of smoothness, geometric continuity is an important problem in the fields of computer aided geo- metric design. It can afford more degrees of freedom for manipulating the shape of curve. Howeve...As an intrinsic measure of smoothness, geometric continuity is an important problem in the fields of computer aided geo- metric design. It can afford more degrees of freedom for manipulating the shape of curve. However, piecewise polynomial functions of geometrically continuous splines are difficult to be constructed. In this paper, the conversion matrix between geometrically con- tinuous spline basis functions and Bezier representation is analyzed. Based on this, construction of arbitrary degree geometrically continuous spline basis functions can be translated into a solution of linear system of equations. The original construction of geomet- rically continuous spline is simplified.展开更多
The explicit expression of the G3 basis function is presented in this paper. It is derived by constructing the conversion matrix between G3 basis function and Brzier representation. After the matrix decomposition, equ...The explicit expression of the G3 basis function is presented in this paper. It is derived by constructing the conversion matrix between G3 basis function and Brzier representation. After the matrix decomposition, equations for constructing G3 splines can be presented independently of geometric shape parameters＇ values. It makes the equation＇s solving easier. It is also known that the general form of the G3spline basis function is given in the first time. Its geometric construction method is presented.展开更多
基金supported by National Natural Science Foundation of China (Nos. 11171180 and 11101303)Specialized Research Fund for the Doctoral Program of Chinese Higher Education (No. 20113705110002)Shandong Provincial Natural Science Foundation (Nos. ZR2010AL005 and ZR2011FL017)
文摘In this paper, we consider the global error bound for the generalized complementarity problem (GCP) with analytic functions. Based on the new technique, we establish computable global error bound under milder conditions, which refines the previously known results.
文摘In this paper,the King’s type modification of(p,q)-Bleimann-Butzer and Hahn operators is defined.Some results based on Korovkin’s approximation theorem for these new operators are studied.With the help of modulus of continuity and the Lipschitz type maximal functions,the rate of convergence for these new operators are obtained.It is shown that the King’s type modification have better rate of convergence,flexibility than classical(p,q)-BBH operators on some subintervals.Further,for comparisons of the operators,we presented some graphical examples and the error estimation in the form of tables through MATLAB(R2015a)
文摘The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of orderα.Applying the Korovkin theorem,we arrive at the convergence of the operator with the aid of moments and central moments.We determine the rate of convergence of the operator using several tools such as K-functional,modulus of continuity,second modulus of continuity.We also give a type of Voronovskaya theorem for estimating error.Moreover,we investigate some results about convergence properties of the operator in a weighted space.Finally,we give numerical examples to support our theorems by using the Maple.
基金Supported by NSFC (No.61100129)Long-span Building Construction Research Project (No.40006014201101)
文摘As an intrinsic measure of smoothness, geometric continuity is an important problem in the fields of computer aided geo- metric design. It can afford more degrees of freedom for manipulating the shape of curve. However, piecewise polynomial functions of geometrically continuous splines are difficult to be constructed. In this paper, the conversion matrix between geometrically con- tinuous spline basis functions and Bezier representation is analyzed. Based on this, construction of arbitrary degree geometrically continuous spline basis functions can be translated into a solution of linear system of equations. The original construction of geomet- rically continuous spline is simplified.
基金Supported by National Natural Science Foundation of China(Grants 61100129)Open Program of Key Laboratory of Intelligent Information Processing,Institute of Computing Technology,Chinese Academy of Sciences(IIP2014-7)
文摘The explicit expression of the G3 basis function is presented in this paper. It is derived by constructing the conversion matrix between G3 basis function and Brzier representation. After the matrix decomposition, equations for constructing G3 splines can be presented independently of geometric shape parameters＇ values. It makes the equation＇s solving easier. It is also known that the general form of the G3spline basis function is given in the first time. Its geometric construction method is presented.
