Abstract: In order to solve the problem that the convergence rate of BP network is not fast, and the neural networks with continuous orthogonal basis cannot approximate discontinuous functions,this paper constructed a class of feed-for- ward neural networks with V orthonormal basis (referred to as V orthogonal network) , and investigated its convergence condition and pseudo-inverse rule. For V system is a class of complete orthonormal systems in I}z(巨。，1习)，and the con- vergence rate of Fourier-V series is comparatively fast, the convergence rate of V orthogonal network is also fast, and it can effectively approximate a class of discontinuous functions of one variable. The simulation results also show that the convergence rate of V orthogonal network is obviously faster than that of 13P network, wavclet network and Legendre network;if using V orthogonal network to approximate the functions whose breakpoints only appear at dyadic rational, its performance of function approximation becomes much better.

Key words: V system, BP network, Wavclct network, I_cgcndrc network, Function approximation