L p approximation capability of radial basis function (RBF) neural networks is investigated. If g: R +1 → R 1 and $g(\parallel x\parallel _{R^n } )$g(\parallel x\parallel _{R^n } ) ∈ L loc p (R n ) with 1 ≤ p < ...L p approximation capability of radial basis function (RBF) neural networks is investigated. If g: R +1 → R 1 and $g(\parallel x\parallel _{R^n } )$g(\parallel x\parallel _{R^n } ) ∈ L loc p (R n ) with 1 ≤ p < ∞, then the RBF neural networks with g as the activation function can approximate any given function in L p (K) with any accuracy for any compact set K in R n , if and only if g(x) is not an even polynomial.展开更多
基金Supported by National Natural Science Foundation of China （Grant No. 10871101） and the Research Fund for the Doctoral Program of Higher Education （Grant No. 20060055010）
文摘In two real Banach spaces, we shall present two conditions, under one of which each nonexpansive mapping must be an isometry.
基金the National Natural Science Foundation of China (10471017)
文摘L p approximation capability of radial basis function (RBF) neural networks is investigated. If g: R +1 → R 1 and $g(\parallel x\parallel _{R^n } )$g(\parallel x\parallel _{R^n } ) ∈ L loc p (R n ) with 1 ≤ p < ∞, then the RBF neural networks with g as the activation function can approximate any given function in L p (K) with any accuracy for any compact set K in R n , if and only if g(x) is not an even polynomial.
