In this article we shall obtain an interpolation formula passing given a serial points and satisfying initial values of the derivatives of higher order in preceding points Finally we shall give the erroneous estimate ...In this article we shall obtain an interpolation formula passing given a serial points and satisfying initial values of the derivatives of higher order in preceding points Finally we shall give the erroneous estimate of the preceding interpolation formula.展开更多
We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algo...We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given.展开更多
为了提高CMAC(cerebellar model articulation controller)神经网络实时在线学习的快速性和准确性,在基于信度分配的CA-CMAC-AMS学习算法的基础上,结合牛顿向前插公式,提出了一种新的CMAC-AMS学习算法(CA-NCMAC-AMS)。数值模拟表明,这种...为了提高CMAC(cerebellar model articulation controller)神经网络实时在线学习的快速性和准确性,在基于信度分配的CA-CMAC-AMS学习算法的基础上,结合牛顿向前插公式,提出了一种新的CMAC-AMS学习算法(CA-NCMAC-AMS)。数值模拟表明,这种CA-NCMAC-AMS的学习算法不但有较快的学习速度和训练精度及建模能力,而且在信号处理、模式识别及高精度的实时智能控制等领域具有很大的应用潜力。展开更多
Interpolation theory is the foundation of finite element methods.In this paper,after reviewing some existed interpolation theorems of anisotropic finite element methods,we present a new way to analyse the interpolatio...Interpolation theory is the foundation of finite element methods.In this paper,after reviewing some existed interpolation theorems of anisotropic finite element methods,we present a new way to analyse the interpolation error of anisotropic elements based on Newton's formula of polynomial interpolation as well as its applications.展开更多
The n-divided difference of the composite function h ：= f o g of functions f, g at a group of nodes t0,t1,…,tn is shown by the combinations of divided differences of f at the group of nodes g（t0）,g（t1）,…,g（tm...The n-divided difference of the composite function h ：= f o g of functions f, g at a group of nodes t0,t1,…,tn is shown by the combinations of divided differences of f at the group of nodes g（t0）,g（t1）,…,g（tm） and divided differences of g at several partial group of nodes t0,t1,…,tn, where m = 1,2,…,n. Especially, when the given group of nodes are equal to each other completely, it will lead to Faà di Bruno＇s formula of higher derivatives of function h.展开更多
In this paper, we consider the higher divided difference of a composite function f（g（t）） in which g（t） is an s-dimensional vector. By exploiting some properties from mixed partial divided differences and multiva...In this paper, we consider the higher divided difference of a composite function f（g（t）） in which g（t） is an s-dimensional vector. By exploiting some properties from mixed partial divided differences and multivariate Newton interpolation, we generalize the divided difference form of Faà di Bruno＇s formula with a scalar argument. Moreover, a generalized Faà di Bruno＇s formula with a vector argument is derived.展开更多
文摘In this article we shall obtain an interpolation formula passing given a serial points and satisfying initial values of the derivatives of higher order in preceding points Finally we shall give the erroneous estimate of the preceding interpolation formula.
基金This paper is a talk on the held in Nanjing, P. R. China, July, 2004.
文摘We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given.
文摘为了提高CMAC(cerebellar model articulation controller)神经网络实时在线学习的快速性和准确性,在基于信度分配的CA-CMAC-AMS学习算法的基础上,结合牛顿向前插公式,提出了一种新的CMAC-AMS学习算法(CA-NCMAC-AMS)。数值模拟表明,这种CA-NCMAC-AMS的学习算法不但有较快的学习速度和训练精度及建模能力,而且在信号处理、模式识别及高精度的实时智能控制等领域具有很大的应用潜力。
基金the National Nutural Science Foundation of China(Grant Nos.10771198,10590353)
文摘Interpolation theory is the foundation of finite element methods.In this paper,after reviewing some existed interpolation theorems of anisotropic finite element methods,we present a new way to analyse the interpolation error of anisotropic elements based on Newton's formula of polynomial interpolation as well as its applications.
基金This work was supported by the National Science Foundation of China （Grant No.10471128）.
文摘The n-divided difference of the composite function h ：= f o g of functions f, g at a group of nodes t0,t1,…,tn is shown by the combinations of divided differences of f at the group of nodes g（t0）,g（t1）,…,g（tm） and divided differences of g at several partial group of nodes t0,t1,…,tn, where m = 1,2,…,n. Especially, when the given group of nodes are equal to each other completely, it will lead to Faà di Bruno＇s formula of higher derivatives of function h.
基金Acknowledgments. This work was supported by the National Science Foundation of China （Grant Nos. 10471128, 10731060）.
文摘In this paper, we consider the higher divided difference of a composite function f（g（t）） in which g（t） is an s-dimensional vector. By exploiting some properties from mixed partial divided differences and multivariate Newton interpolation, we generalize the divided difference form of Faà di Bruno＇s formula with a scalar argument. Moreover, a generalized Faà di Bruno＇s formula with a vector argument is derived.
