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A methodology for mapping numerical algorithms into systolic arrays is presented in this paper. This mapping is done using a transformation function which transforms the original sequential algorithm into a suitable parallel form. A program was developed to automatically generate this transformation. We consider both the case of arbitrarily large systolic arrays as well as the more realistic case of fixed-size systolic arrays requiring algorithm partitioning. An example of the algorithm is given to present the methodology and the results obtained with the program.