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In this paper, in order to optimize neural network architecture and generalization, after analyzing the reasons of overfitting and poor generalization of the neural networks, we presented a class of constructive decay RBF neural networks to repair the singular value of a continuous function with finite number of jumping discontinuity points. We proved that a function with m jumping discontinuity points can be approximated by a simplest neural network and a decay RBF neural network in L^2(@?) by each @? error, and a function with m jumping discontinuity point y=f(x),x@?E@?@?^d can be constructively approximated by a decay RBF neural network in L^2(@?^d) by each @e0 error. Then the whole networks will have less hidden neurons and well generalization in the same of the first part. A real world problem about stock closing price with jumping discontinuity have been presented and verified the correctness of the theory.