A note on the perturbation bound of the Drazin inverse
\textit{N. Gonzalez}, \textit{J. Koliha} and \textit{Y. Wei} [Linear Algebra Appl. 312, 181-189 (2000; Zbl 0963.15002)] or \textit{Y. Wei} [Appl. Math. Comput. 125, 231-244 (2002; Zbl 1025.15004)] have derived bounds for \(\|(A+E)^\#-A^D\|\) where \((\cdot)^\#\) denotes the group inverse and \((\cdot)^D\) denotes the Drazin inverse. These bounds hold when among other conditions, the index of \(A+E\) is 1. In this paper, the latter condition is removed and sharper bounds are obtained (unlike in the previous references, the bound is small when \(\|E\|\) is small). As a special case, a bound is given when \((\cdot)^\#\) is replaced by \((\cdot)^D\).
scientific article; zbMATH DE number 1978085