Concise systolic algorithms for linear systems

Concise algorithms to compute a solution of a system of m linear equations Ax=b with n variables are presented. It is matrix inversion free. It provides an in built consistency check and also produces the rank of the matrix A. It converts A into a full rank matrix, thus preserving the complete information of the system. Four designs based on systolic processor arrays are presented and their scope is discussed. The first one is the Leiserson systolic design while the remaining three, viz. the double pipe design the fitted diagonal design, and the folding design are derived versions of the first design with improved performanc