@article {IOPORT.06049689,
    author       = {Chang, Xiao-Wen and Li, Ren-Cang},
    title        = {Multiplicative perturbation analysis for QR factorizations.},
    year         = {2011},
    journal      = {Numerical Algebra, Control and Optimization},
    volume       = {1},
    number       = {2},
    issn         = {2155-3289},
    pages        = {301-316},
    publisher    = {American Institute of Mathematical Sciences (AIMS), Springfield, MO},
    doi          = {10.3934/naco.2011.1.301},
    abstract     = {The QR-factorization of an $m$ by $n$ matrix $A$ is the following: $A = QR$, where $Q$ has orthogonal columns and $R$ is upper triangular with positive diagonal entries. This factorization is uniquely defined if $m \ge n$ and $A$ has full column rank. The question studied here is what happens to the QR factors if A is multiplicatively perturbed. The main results are given here in Chapter 3. If the perturbation is multiplication from the left by an $m$-by-$m$ matrix $D_L$ then the relative changes in the factors Q and R are bounded by a small constant multiple of the Frobenius norm of $I-D_L$. If the perturbation is a multiplication from the right then the factors of the first order bounds contain the condition numbers of the scaled R-factor. Several improved versions of these results are given which are better if the perturbations are not so near to the identity. Two sets of numerical examples are shown.},
    reviewer     = {Ludwig Elsner (Bielefeld)},
    identifier   = {06049689},
}