Abstract:
Interpolation problem by a wavelet neural network is discussed.In 1-dimension case, for given 1-dimensional interpolated samples, a single hidden layer feed-forward neural network (called a wavelet neural network, WNN) is constructed by using a continuous wavelet function as the activation function.Under certain condition, the existence of the exact interpolation wavelet neural network (EIWNN) is proved first, and the approximate interpolation wavelet neural network (AIWNN) is constructed.Meanwhile, an estimation of the deviation between EIWNN and AIWNN is obtained.For given multi-dimensional interpolated samples, by considering the inner products of the interpolation nodes and some point and using the obtained results for 1-dimension case, the exact and approximate interpolation wavelet neural networks are constructed, and an estimation of the deviation between them is proved.
