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Taking full advantage of pipeline architecture, we propose a fast solution method of sparse network equations that consists of an improved node ordering and data storing scheme. The improved node ordering scheme enables overlapped operation of a series of multiply-and-subtract calculations in the substitution process by deriving parallelism in them. The new data storing scheme stores factorized data and the address of variables in vector. Using these new schemes in array processor AP-120B, the substitution process of solving network equations can be executed three times as fast as with the conventional method supplied in the AP-120B's standard mathematical library.