TY - JOUR
ID - 1256
TI - Perturbation bounds for $g$-inverses with respect to the unitarily invariant norm
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Meng, L.
AD - College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, P.R. China.
Y1 - 2017
PY - 2017
VL - 43
IS - 7
SP - 2655
EP - 2662
KW - $g$-inverse
KW - additive perturbation bound
KW - multiplicative perturbation bound
KW - unitarily invariant norm
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_1256.html
L1 - http://bims.iranjournals.ir/article_1256_48f9f6287f956af831c7368cb1ae09b4.pdf
ER -