A New Perturbation Bound for the LDU Factorization of Diagonally Dominant Matrices Articles uri icon

publication date

  • July 2014

start page

  • 904

end page

  • 930

issue

  • 3

volume

  • 35

International Standard Serial Number (ISSN)

  • 0895-4798

Electronic International Standard Serial Number (EISSN)

  • 1095-7162

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.

keywords

  • accurate computations; column diagonal dominance pivoting; diagonally dominant matrices; diagonally dominant parts; ldu factorization; rank-revealing decomposition; relative perturbation theory