%0 Journal Article
%T Perturbation bounds for $g$-inverses with respect to the unitarily invariant norm
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Meng, L.
%D 2017
%\ 12/30/2017
%V 43
%N 7
%P 2655-2662
%! Perturbation bounds for $g$-inverses with respect to the unitarily invariant norm
%K $g$-inverse
%K additive perturbation bound
%K multiplicative perturbation bound
%K unitarily invariant norm
%R
%X Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest perturbed $g$-inverse. These results generalize and improve the existing results published recently to some extent.
%U http://bims.iranjournals.ir/article_1256_48f9f6287f956af831c7368cb1ae09b4.pdf