A new class of parallel algorithms for solving systems of linear equations

In this paper a class of novel feed-forward direct methods is presented for solving nonsingular systems of linear equations. The computational complexity of these methods is in the order of an $LU$, $QR$, or $LL^t $ matrix factorization. This is also true for the complexity of their systolic implementations. Unlike the direct methods of factorization followed by backsubstitution, the systolic implementations of the novel methods do not suffer from the backsubstitution bottleneck. A numerically stable and robust method, which uses only Givens rotations as elementary operations, is included in the class.