Using the equivalence relation between K-functional and moduli of smoothness, methods of partition function and induction, we establish a strong direct theorem and an inverse theorem of weak type of weighted approxima...Using the equivalence relation between K-functional and moduli of smoothness, methods of partition function and induction, we establish a strong direct theorem and an inverse theorem of weak type of weighted approximation for d-dimensional Bernstein operators on a simplex in this paper.展开更多
This paper presents learning rates for the least-square regularized regression algorithms with polynomial kernels. The target is the error analysis for the regression problem in learning theory. A regularization schem...This paper presents learning rates for the least-square regularized regression algorithms with polynomial kernels. The target is the error analysis for the regression problem in learning theory. A regularization scheme is given, which yields sharp learning rates. The rates depend on the dimension of polynomial space and polynomial reproducing kernel Hilbert space measured by covering numbers. Meanwhile, we also establish the direct approximation theorem by Bernstein-Durrmeyer operators in $ L_{\rho _X }^2 $ with Borel probability measure.展开更多
For weighted approximation in Lp-norm,we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Bernstein operators sequence on the r-fold integr...For weighted approximation in Lp-norm,we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Bernstein operators sequence on the r-fold integrated Wiener space.展开更多
In this paper we give equivalent theorems on simultaneous approximation for the combinations of Bernstein operators by r-th Ditzian- Totik modulus of smoothness w^rφλ （f, t）（0 ≤ λ≤ 1）. We also investigate th...In this paper we give equivalent theorems on simultaneous approximation for the combinations of Bernstein operators by r-th Ditzian- Totik modulus of smoothness w^rφλ （f, t）（0 ≤ λ≤ 1）. We also investigate the relation between the derivatives of the combinations of Bernstein operators and the smoothness of derivatives of functions.展开更多
文摘Using the equivalence relation between K-functional and moduli of smoothness, methods of partition function and induction, we establish a strong direct theorem and an inverse theorem of weak type of weighted approximation for d-dimensional Bernstein operators on a simplex in this paper.
文摘This paper presents learning rates for the least-square regularized regression algorithms with polynomial kernels. The target is the error analysis for the regression problem in learning theory. A regularization scheme is given, which yields sharp learning rates. The rates depend on the dimension of polynomial space and polynomial reproducing kernel Hilbert space measured by covering numbers. Meanwhile, we also establish the direct approximation theorem by Bernstein-Durrmeyer operators in $ L_{\rho _X }^2 $ with Borel probability measure.
文摘For weighted approximation in Lp-norm,we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Bernstein operators sequence on the r-fold integrated Wiener space.
基金Supported by the Key Academic Discipline of Zhejiang Provincial of China under Grant No.2005.
文摘In this paper we give equivalent theorems on simultaneous approximation for the combinations of Bernstein operators by r-th Ditzian- Totik modulus of smoothness w^rφλ （f, t）（0 ≤ λ≤ 1）. We also investigate the relation between the derivatives of the combinations of Bernstein operators and the smoothness of derivatives of functions.
