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<正>A gradient neural network(GNN) for solving online a set of simultaneous linear equations is generalized and investigated in this paper.Instead of the earlier-presented asymptotical convergence,global exponential convergence could be proved for such a class of neural networks.In addition, superior convergence could be achieved using power-sigmoid activation-functions,compared with using linear activation-functions. Computer-simulation results substantiate further the above analysis and efficacy of such neural networks.