共同光滑函数类的逼近特征
发布时间：2019-06-18 20:46
【摘要】：本文将再生核Hilbert空间作为假设空间,通过整函数和节点函数的逼近结果来研究逆二次项核和Gaussian核在共同光滑函数类中产生的逼近误差,得到其逼近误差呈对数型衰减。即:(1)对逆二次项核(?)时,有(?)。(2)对Gaussian核(?),当(?)时,有(?)。其中f∈W~A_2(IR~d),r定义见1.1。这一结果推广了周定轩对逆二次项核和Gaussian核在一般Sobolev空间中的逼近误差的研究结果。
[Abstract]:In this paper, the reproducing kernel Hilbert space is taken as the hypothetical space, and the approximation error of inverse quadratic kernel and Gaussian kernel in the common smooth function class is studied by using the approximation results of the whole function and the node function, and it is found that the approximation error is logarithmic decay. That is, (1) for the inverse quadratic kernel (?) There is (?). (2) for the Gaussian kernel (?), when (?) When, there is (?). Where f 鈮，
本文编号：2501780
[Abstract]:In this paper, the reproducing kernel Hilbert space is taken as the hypothetical space, and the approximation error of inverse quadratic kernel and Gaussian kernel in the common smooth function class is studied by using the approximation results of the whole function and the node function, and it is found that the approximation error is logarithmic decay. That is, (1) for the inverse quadratic kernel (?) There is (?). (2) for the Gaussian kernel (?), when (?) When, there is (?). Where f 鈮，
本文编号：2501780
本文链接：https://www.wllwen.com/kejilunwen/yysx/2501780.html
