Rigorous Perturbation Bounds of Some Matrix
Factorizations
Xiao-Wen Chang and Damien Stehlé
Abstract: This article presents rigorous normwise perturbation bounds for the
Cholesky, LU and QR factorizations with normwise or componentwise
perturbations in the given matrix. The considered componentwise
perturbations have the form of backward rounding errors for the
standard factorization algorithms. The used approach is a combination
of the classic and refined matrix equation approaches. Each of the
new rigorous perturbation bounds is a small constant multiple of the
corresponding first-order perturbation bound obtained by the refined
matrix equation approach in the literature and can be estimated
efficiently. These new bounds can be much tighter than the existing
rigorous bounds obtained by the classic matrix equation approach,
while the conditions for the former to hold are almost as moderate as
the conditions for the latter to hold.
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