In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results fo...In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results for the simultaneous approx- imation, with the same order of accuracy, of a function and its derivatives （whenever these exist）, are obtained. The relation with neural networks and radial basis func- tions approximations is discussed. Numerical examples are given for the purpose of illustration.展开更多
In this paper, we introduce a type of approximation operators of neural networks with sigmodal functions on compact intervals, and obtain the pointwise and uniform estimates of the ap- proximation. To improve the appr...In this paper, we introduce a type of approximation operators of neural networks with sigmodal functions on compact intervals, and obtain the pointwise and uniform estimates of the ap- proximation. To improve the approximation rate, we further introduce a type of combinations of neurM networks. Moreover, we show that the derivatives of functions can also be simultaneously approximated by the derivatives of the combinations. We also apply our method to construct approximation operators of neural networks with sigmodal functions on infinite intervals.展开更多
基金supported, in part, by the GNAMPA and the GNFM of the Italian INdAM
文摘In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results for the simultaneous approx- imation, with the same order of accuracy, of a function and its derivatives （whenever these exist）, are obtained. The relation with neural networks and radial basis func- tions approximations is discussed. Numerical examples are given for the purpose of illustration.
基金Supported by National Natural Science Foundation of China(Grant No.10901044)Qianjiang Rencai Program of Zhejiang Province(Grant No.2010R10101)+1 种基金Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education MinistryProgram for Excellent Young Teachers in Hangzhou Normal University
文摘In this paper, we introduce a type of approximation operators of neural networks with sigmodal functions on compact intervals, and obtain the pointwise and uniform estimates of the ap- proximation. To improve the approximation rate, we further introduce a type of combinations of neurM networks. Moreover, we show that the derivatives of functions can also be simultaneously approximated by the derivatives of the combinations. We also apply our method to construct approximation operators of neural networks with sigmodal functions on infinite intervals.
