Abstract. This work introduces a new perturbation bound for the L factor of the LDU factorization of (row) diagonally dominant matrices computed via the column diagonal dominance pivoting strategy. This strategy yields L and U factors which are always well-conditioned and, so, the LDU factorization is guaranteed to be a rank-revealing decomposition. The new bound together with those for the D and U factors in [F. M. Dopico and P. Koev, Numer. Math., 119 (2011), pp. 337-371] establish that if diagonally dominant matrices are parameterized via their diagonally dominant parts and off-diagonal entries, then tiny relative componentwise perturbations of these parameters produce tiny relative normwise variations of L and U and tiny relative entrywise variations of D when column diagonal dominance pivoting is used. These results will allow us to prove in a follow-up work that such perturbations also lead to strong perturbation bounds for many other problems involving diagonally dominant matrices.Key words. accurate computations, column diagonal dominance pivoting, diagonally dominant matrices, diagonally dominant parts, LDU factorization, rank-revealing decomposition, relative perturbation theory AMS subject classifications. 65F05, 65F15, 15A18, 15A23, 15B99 DOI. 10.1137/13093858X1. Introduction. Perturbation analysis is a classical topic in matrix theory and numerical linear algebra [23,24,35] which still attracts a lot of attention. In recent years, considerable effort has been devoted to deriving sharper perturbation bounds when structured perturbations of important classes of structured matrices are considered (see, as a sample, [1,3,4,7,12,14,18,21,22,26,27,28,29,30,31,33,34,37,38,40]). In this paper, we present a new perturbation bound for the L factor of the LDU factorization of diagonally dominant matrices under a class of componentwise structure-preserving perturbations which are important in numerical computations [14,39,40]. Here, A = LDU is an LDU factorization of A if L is a unit lower triangular matrix, D is a diagonal matrix, and U is a unit upper triangular matrix.Solution of this problem is motivated by several facts. First, apart from its classical applications [20], the LDU factorization has been applied recently to computing accurate rank-revealing decompositions (RRD) [11] of many classes of structure matrices, which are used to perform matrix computations with high relative accuracy [5,11,13,15,17]. In this context, an LDU factorization is an RRD if L and U are well-conditioned. A key point in computing an LDU factorization as an RRD is that the standard partial pivoting strategy does not produce, in general, well-conditioned factors L and U , and that neither complete nor rook pivoting guarantees that L and