Abstract
This paper provides additive perturbation bounds for the generalized core inverse A d , † of a complex matrix A. Given perturbation matrix E, we first present upper bounds for ‖ ( A + E ) d , † − A d , † ‖ 2 ‖ A d , † ‖ 2 under the condition R ( E ) ⊆ R ( A k ) , N ( A k A † ) ⊆ N ( E ) , where k = ind ( A ) , and then under the condition ( A + E ) ( A + E ) d , † = A A d , † . We then explore an integral formula for the generalized core inverse of a perturbed matrix associated with a semi-stable matrix. Furthermore, a perturbation bound for ‖ ( A + E ) d , † − A d , † ‖ F is obtained without conditions. Sufficient conditions for the continuity of the generalized core inverse can be obtained as a result. Finally, numerical examples are presented to illustrate the derived bounds.
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