Publication: A new perturbation bound for the LDU factorization of diagonally dominant matrices
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2014-07
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Society for Industrial and Applied Mathematics
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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.
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Accurate computations, column diagonal dominance pivoting, diagonally dominant matrices, LDU factorization, rank-revealing decomposition, relative perturbation theory, diagonally dominant parts
Bibliographic citation
SIAM Journal on Matrix Analysis and Applications, 35 (2014) 3, pp. 904-930.