Systolic Gaussian elimination over GF(p) with partial pivoting

摘要

A systolic architecture is proposed for the triangularization by means of the Gaussian elimination algorithm 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 elimination with partial pivoting, although the operation of the array remains purely systolic. Extension of the array to the complete solution of a linear system Ax=b over GF(p) is also considered.