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A parallel processor system and its mode of operation are described. A notation for writing programs on it is introduced. Methods for iterative solution of a set of linear equations are then discussed. The well-known algorithms of Jacobi and Gauss–Seidel are parallelized despite the apparent inherent sequentiality of the latter. New, parallel methods for the iterative solution of linear equations are introduced and their convergence is discussed. A measure of speedup is computed for all methods. It shows that in most cases the algorithms developed in the paper may be efficiently executed on a parallel processor system.