The aim of the paper is to estimate the density functions or distribution functions measured by Wasserstein metric, a typical kind of statistical distances, which is usually required in the statistical learning. Based...The aim of the paper is to estimate the density functions or distribution functions measured by Wasserstein metric, a typical kind of statistical distances, which is usually required in the statistical learning. Based on the classical Bernstein approximation, a scheme is presented. To get the error estimates of the scheme, the problem turns to estimating the L1 norm of the Bernstein approximation for monotone C-1 functions, which was rarely discussed in the classical approximation theory. Finally, we get a probability estimate by the statistical distance.展开更多
In actuarial science, Panjer recursion （1981） is used in insurance to compute the loss distribution of the compound risk models. When the severity distribution is continuous with density function, numerical calculat...In actuarial science, Panjer recursion （1981） is used in insurance to compute the loss distribution of the compound risk models. When the severity distribution is continuous with density function, numerical calculation for the compound distribution by applying Panjer recursion will involve an approxi- mation of the integration. In order to simplify the numerical algorithms, we apply Bernstein approximation for the continuous severity distribution function and obtain approximated recursive equations, which are used for computing the approximated values of the compound distribution. The theoretical error bound for the approximation is also obtained. Numerical results show that our algorithm provides reliable results.展开更多
In this paper we investigate simultaneous approximation for arbitrary system of nodes on smooth domain in complex plane. Some results which are better than those of known theorems are obtained.
We prove a pointwise characterization result for combinations of Bernstein polynomials. The main result of this paper includes an equivalence theorem of H. Berens and G. G. Lorentz as a special case.
In this work we slwly linear polynomial operators preserving some consecutive i-convexities and leaving in-verant the polynomtals up to a certain degree. First we study the existence of an incompatibility between the ...In this work we slwly linear polynomial operators preserving some consecutive i-convexities and leaving in-verant the polynomtals up to a certain degree. First we study the existence of an incompatibility between the conservation of cenain i-cotivexities and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DcVore about the Bernstein's operator ts extended. Finally, from these results a genera'ized Bernstein's operator is obtained.展开更多
We introduce a new type of modified Bernstein quasi-interpolants, which can be used to approximate functions with singularities. We establish direct, inverse, and equivalent theorems of the weighted approximation of t...We introduce a new type of modified Bernstein quasi-interpolants, which can be used to approximate functions with singularities. We establish direct, inverse, and equivalent theorems of the weighted approximation of this modified quasi-interpolants. Some classical results on approximation of continuous functions are generalized to the weighted approximation of functions with singularities.展开更多
With the deteriorating effects resulting from global warming in many areas, geographically distributed data centers contribute greatly to carbon emissions, because the major energy supply is fossil fuels. Considering ...With the deteriorating effects resulting from global warming in many areas, geographically distributed data centers contribute greatly to carbon emissions, because the major energy supply is fossil fuels. Considering this issue, many geographically distributed data centers are attempting to use clean energy as their energy supply, such as fuel cells and renewable energy sources. However, not all workloads can be powered by a single power sources, since different workloads exhibit different characteristics. In this paper, we propose a fine-grained heterogeneous power distribution model with an objective of minimizing the total energy costs and the sum of the energy gap generated by the geographically distributed data centers powered by multiple types of energy resources. In order to achieve these two goals, we design a two-stage online algorithm to leverage the power supply of each energy source. In each time slot, we also consider a chance-constraint problem and use the Bernstein approximation to solve the problem. Finally, simulation results based on real-world traces illustrate that the proposed algorithm can achieve satisfactory performance.展开更多
基金Supported by 973-Project of China(2006cb303102)the National Science Foundation of China(11461161006,11201079)
文摘The aim of the paper is to estimate the density functions or distribution functions measured by Wasserstein metric, a typical kind of statistical distances, which is usually required in the statistical learning. Based on the classical Bernstein approximation, a scheme is presented. To get the error estimates of the scheme, the problem turns to estimating the L1 norm of the Bernstein approximation for monotone C-1 functions, which was rarely discussed in the classical approximation theory. Finally, we get a probability estimate by the statistical distance.
文摘In actuarial science, Panjer recursion （1981） is used in insurance to compute the loss distribution of the compound risk models. When the severity distribution is continuous with density function, numerical calculation for the compound distribution by applying Panjer recursion will involve an approxi- mation of the integration. In order to simplify the numerical algorithms, we apply Bernstein approximation for the continuous severity distribution function and obtain approximated recursive equations, which are used for computing the approximated values of the compound distribution. The theoretical error bound for the approximation is also obtained. Numerical results show that our algorithm provides reliable results.
文摘In this paper we investigate simultaneous approximation for arbitrary system of nodes on smooth domain in complex plane. Some results which are better than those of known theorems are obtained.
文摘We prove a pointwise characterization result for combinations of Bernstein polynomials. The main result of this paper includes an equivalence theorem of H. Berens and G. G. Lorentz as a special case.
基金This work was supported by Junta de Andalucia. Grupo de investigacion Matematica Aplioada. Codao 1107
文摘In this work we slwly linear polynomial operators preserving some consecutive i-convexities and leaving in-verant the polynomtals up to a certain degree. First we study the existence of an incompatibility between the conservation of cenain i-cotivexities and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DcVore about the Bernstein's operator ts extended. Finally, from these results a genera'ized Bernstein's operator is obtained.
文摘We introduce a new type of modified Bernstein quasi-interpolants, which can be used to approximate functions with singularities. We establish direct, inverse, and equivalent theorems of the weighted approximation of this modified quasi-interpolants. Some classical results on approximation of continuous functions are generalized to the weighted approximation of functions with singularities.
基金supported in part by National Natural Science Foundation of China (No. 61772286, No. 61802208)China Postdoctoral Science Foundation(No. 2019M651923)+2 种基金Natural Science Foundation of Jiangsu Province of China(No. BK20191381)Primary Research&Development Plan of Jiangsu Province(No. BE2019742)Natural Science Fund for Colleges and Universities in Jiangsu Province (No. 18KJB520036)。
文摘With the deteriorating effects resulting from global warming in many areas, geographically distributed data centers contribute greatly to carbon emissions, because the major energy supply is fossil fuels. Considering this issue, many geographically distributed data centers are attempting to use clean energy as their energy supply, such as fuel cells and renewable energy sources. However, not all workloads can be powered by a single power sources, since different workloads exhibit different characteristics. In this paper, we propose a fine-grained heterogeneous power distribution model with an objective of minimizing the total energy costs and the sum of the energy gap generated by the geographically distributed data centers powered by multiple types of energy resources. In order to achieve these two goals, we design a two-stage online algorithm to leverage the power supply of each energy source. In each time slot, we also consider a chance-constraint problem and use the Bernstein approximation to solve the problem. Finally, simulation results based on real-world traces illustrate that the proposed algorithm can achieve satisfactory performance.
