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We present an efficient algorithm for reverse engineering gene regulatory networks from microarray datasets using linear system of ordinary differential equations to deal with issues of underdetermined and ill-conditioned datasets. Our method was evaluated in in silico experiments. It was shown that the method can be readily applied to reconstruct the sparse network structure for a linear system with relatively small number of measurements. The algorithm can be also used to reconstruct partial network structure with extremely small number of measurements. The method was successfully applied to predict networks and to interpret yeast cell cycle gene expression data.