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A new perturbation bound for the LDU factorization of diagonally dominant matrices

Dailey, Megan; Martínez Dopico, Froilán C.; Ye, Qiang
Fonte: Society for Industrial and Applied Mathematics Publicador: Society for Industrial and Applied Mathematics
Tipo: info:eu-repo/semantics/publishedVersion; info:eu-repo/semantics/article
Publicado em /07/2014 ENG
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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.; Research supported in part by Ministerio de Economía y Competitividad of Spain under grant MTM2012-32542.