SYSTOLIC TRIANGULARIZATION OVER FINITE-FIELDS

We propose a systolic architecture for the triangularization of large dense n × n matrices over GF(p), where p is a prime number. The solution of large dense linear systems over GF(p) is the major computational step in various algorithms issuing from arithmetic number theory and computer algebra. The proposed architecture implements the triangularization via a new algorithm as robust as Gaussian elimination with partial pivoting, and the operation of the array remains purely systolic. The algorithm triangularizes a dense n × n matrix in time 2n on a triangular array of n (n + 1) 2 elementary processors, which is (to our knowledge) the best area-time performance. © 1990.