In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,w...In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,we also get some other results about the mean approximation.展开更多
Ⅰ. INTRODUCTION Let ∑<sub>n</sub>= {u∈R<sup>n+1</sup>; |u|=1} be the unit sphere in （n+1）dimensional Euclidean space. For any functionf on ∑<sub>n</sub>, we associate its expa...Ⅰ. INTRODUCTION Let ∑<sub>n</sub>= {u∈R<sup>n+1</sup>; |u|=1} be the unit sphere in （n+1）dimensional Euclidean space. For any functionf on ∑<sub>n</sub>, we associate its expansion in spherical harmonics:展开更多
In this paper, the technique of approximate partition of unity is used to construct a class of neural networks operators with sigmoidal functions. Using the modulus of continuity of function as a metric, the errors of...In this paper, the technique of approximate partition of unity is used to construct a class of neural networks operators with sigmoidal functions. Using the modulus of continuity of function as a metric, the errors of the operators approximating continuous functions defined on a compact interval are estimated. Furthmore, Bochner-Riesz means operators of double Fourier series are used to construct networks operators for approximating bivariate functions, and the errors of approximation by the operators are estimated.展开更多
文摘In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,we also get some other results about the mean approximation.
基金Project supported by the National Natural Science Foundation of China
文摘Ⅰ. INTRODUCTION Let ∑<sub>n</sub>= {u∈R<sup>n+1</sup>; |u|=1} be the unit sphere in （n+1）dimensional Euclidean space. For any functionf on ∑<sub>n</sub>, we associate its expansion in spherical harmonics:
基金Supported by the National Natural Science Foundation of China(61179041, 61101240)the Zhejiang Provincial Natural Science Foundation of China(Y6110117)
文摘In this paper, the technique of approximate partition of unity is used to construct a class of neural networks operators with sigmoidal functions. Using the modulus of continuity of function as a metric, the errors of the operators approximating continuous functions defined on a compact interval are estimated. Furthmore, Bochner-Riesz means operators of double Fourier series are used to construct networks operators for approximating bivariate functions, and the errors of approximation by the operators are estimated.
