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An algorithm for the parallel solution of large sparse sets of linear equations, given their factor matrices, is developed. It is aimed at efficient practical implementation on a processor of the multiple instruction multiple data stream (MIMD) type. The software required to implement the algorithm is described. In addition, the amount of memory necessary for data retention during execution is considered and related to that which is required on single processor systems. Hardware developed for the implementation of the algorithm is described. Bus contention for the system is outlined and shown to be insignificant. Possible bus contention problems for systems differing in the number of processors and speed of processing elements are also considered. A simulator modeling the execution of the algorithm on large systems has been implemented. The performance of the algorithm, in terms of execution speed enhancement relative to the theoretical maximum, is shown to be good.