This paper presents a fast layer-wise linearized algorithm for feedforward neural networks by mathematic methods with the following features:constructing target function for each layer by new methods;not calculating the Hessian matrix

thus greatly reducing the learning time.Simulation shows that the new algorithm can accelerate the convergence rate and reduce the error compared with the existing algorithms such as backpropagation (BP) algorithm

BP algorithm with momentum factor and existing layer-wise algorithms.