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.
