This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of...This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next).展开更多
This paper solves the two dimensional linear Fredholm integral equations of the second kind by combining the meshless barycentric Lagrange interpolation functions and the Gauss-Legendre quadrature formula. Inspired by...This paper solves the two dimensional linear Fredholm integral equations of the second kind by combining the meshless barycentric Lagrange interpolation functions and the Gauss-Legendre quadrature formula. Inspired by this thought, we convert the equations into the associated algebraic equations. The results of the numerical examples are given to illustrate that the approximated method is feasible and efficient.展开更多
This paper deals with the description and the representation of polynomials defined over n-simplices, The polynomials are computed by using two recurrent schemes: the Neville-Aitken one for the Lagrange interpolating ...This paper deals with the description and the representation of polynomials defined over n-simplices, The polynomials are computed by using two recurrent schemes: the Neville-Aitken one for the Lagrange interpolating operator and the De Casteljau one for the Bernstein-Bezier approximating operator. Both schemes fall intothe framework of transformations of the form where the F iare given numbers (forexample, at the initial step they coincide with the values of the function on a given lattice), and the coefficients (x) are linear polynomials valued in x and x is fixed. A general theory for such sequence of transformations can be found in [2] where it is also proved that these tranformations are completely characterized in term of a linear functional, reference functional. This functional is associated with a linear space., characteristic space.The concepts of reference functionals and characteristic spaces will be used and we shall prove the existence of a characteristic space for the reference functional: associated with these operators.展开更多
In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality o...In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.展开更多
为了进一步提高编码速度,促进视频编码技术在多媒体通信领域的实际应用,本文对率失真视频编码的关键算法进行了深入的研究并提出了其优化方法,并从信息论理论出发,着重围绕图像压缩的理论,利用率失真特征数学模型、拉格朗日乘子法,对目...为了进一步提高编码速度,促进视频编码技术在多媒体通信领域的实际应用,本文对率失真视频编码的关键算法进行了深入的研究并提出了其优化方法,并从信息论理论出发,着重围绕图像压缩的理论,利用率失真特征数学模型、拉格朗日乘子法,对目前新一代的H.264视频标准进行编码算法模式选择,试图从最根本的理论角度探讨信源编码,以便得到更高的压缩比、更好的图像质量和更快的编码速度。最后,利用本文提出的编码模式优化算法,对H.264的J M61e(JUT Test Model)系统测试模型的性能进行全面测试。展开更多
基金The second named author was supported in part by an NSERC Postdoctoral Fellowship,Canada and a CR F Grant,University of Alberta
文摘This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next).
文摘This paper solves the two dimensional linear Fredholm integral equations of the second kind by combining the meshless barycentric Lagrange interpolation functions and the Gauss-Legendre quadrature formula. Inspired by this thought, we convert the equations into the associated algebraic equations. The results of the numerical examples are given to illustrate that the approximated method is feasible and efficient.
文摘This paper deals with the description and the representation of polynomials defined over n-simplices, The polynomials are computed by using two recurrent schemes: the Neville-Aitken one for the Lagrange interpolating operator and the De Casteljau one for the Bernstein-Bezier approximating operator. Both schemes fall intothe framework of transformations of the form where the F iare given numbers (forexample, at the initial step they coincide with the values of the function on a given lattice), and the coefficients (x) are linear polynomials valued in x and x is fixed. A general theory for such sequence of transformations can be found in [2] where it is also proved that these tranformations are completely characterized in term of a linear functional, reference functional. This functional is associated with a linear space., characteristic space.The concepts of reference functionals and characteristic spaces will be used and we shall prove the existence of a characteristic space for the reference functional: associated with these operators.
文摘In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.
文摘为了进一步提高编码速度,促进视频编码技术在多媒体通信领域的实际应用,本文对率失真视频编码的关键算法进行了深入的研究并提出了其优化方法,并从信息论理论出发,着重围绕图像压缩的理论,利用率失真特征数学模型、拉格朗日乘子法,对目前新一代的H.264视频标准进行编码算法模式选择,试图从最根本的理论角度探讨信源编码,以便得到更高的压缩比、更好的图像质量和更快的编码速度。最后,利用本文提出的编码模式优化算法,对H.264的J M61e(JUT Test Model)系统测试模型的性能进行全面测试。
