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New advancement in microarray technologies has made it possible to reconstruct gene regulation networks from mass gene expression data measured by microarray. Typically, gene regulation networks are sparse networks. This sparse topology knowledge can be exploited to develop algorithms for network reconstruction. In this direction, a method called network component analysis (NCA) has been developed recently. A major disadvantage of the original NCA algorithm is that it is very time consuming, and it also has convergence problem as an iterative approach. In this paper we propose several fast, non-iterative NCA algorithms. They are basically based on matrix computation. The algorithms demonstrate good performance when applied to a hypothetical and a real gene regulation network.