The Research On Neural Network With Complex-variable Weight Function And Its Application

In the real number field and complex number field the traditional network learning algorithm (such as BP algorithm, RBF algorithm) exist many defects, such as local minima, slow convergence, difficult to obtain the global optimal point and the constant weights which are difficult to reflect the sample information; and in the practical application of traditional neural network model is difficult to determine. Based on those defects, a new model and algorithm, named complex-variable weight functions neural networks, is proposed in the monograph,"The new neural networks theory and method". The new algorithm has overcome the tradition neural network learning algorithm's flaws and simplified the network architecture. Moreover, along with samples increase in the number, the network's generalization ability is also enhanced.Complex weight function neural network has the characteristics of weight functions neural networks, and it's the implementation of the weight functions neural networks in the complex field. In the theory part, the approximation problem of the complex Lagrange interpolation based on the Fejér points is given; after that, the model and the weight function are determine of the complex weight function neural network; then analyze the error of the network; Finally, we can conclude that complex weight function neural network has high accuracy and convergence speed through simulation experiments, which is compared with conventional BP, RBF neural networks algorithm.In the application part, the FIR filter design is given, which based on the complex weight function neural network. First the design model is given; then on the basis, the simulation experiments are given which based on the complex weight function neural network algorithm and the BP algorithm; at the last part, by comparing the simulation results, we can find that the new algorithm in this paper have good results.