Perturbation bounds for triangular and full rank factorizations

We give componentwise bounds for the perturbations of the LU and LDU factorizations.These bounds are valid for all perturbations which keeps nonsingularity and LU-factorizability. It is shown that the new perturbation bounds are sharper than the earlier results. The perturbation bounds are then applied to full rank factorizations produced by the rank reduction procedure. The result indicates that these full rank factorizations are stable if the LDU factorization of a certain matrix is also stable.