Analytic perturbation of generalized inverses

Konstantin Avrachenkov 1 Jean-Bernard Lasserre 2
1 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
Abstract : We investigate the analytic perturbation of generalized inverses. Firstly we analyze the analytic perturbation of the Drazin generalized inverse (also known as reduced resolvent in operator theory). Our approach is based on spectral theory of linear operators as well as on a new notion of group reduced resolvent. It allows us to treat regular and singular perturbations in a unified framework. We provide an algorithm for computing the coefficients of the Laurent series of the perturbed Drazin generalized inverse. In particular, the regular part coefficients can be efficiently calculated by recursive formulae. Finally we apply the obtained results to the perturbation analysis of the Moore-Penrose generalized inverse in the real domain.
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Linear Algebra and its Applications, Elsevier, 2013, 438 (4), pp.1793-1813. 〈http://www.sciencedirect.com/science/article/pii/S0024379511007348〉. 〈10.1016/j.laa.2011.10.037〉
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Konstantin Avrachenkov, Jean-Bernard Lasserre. Analytic perturbation of generalized inverses. Linear Algebra and its Applications, Elsevier, 2013, 438 (4), pp.1793-1813. 〈http://www.sciencedirect.com/science/article/pii/S0024379511007348〉. 〈10.1016/j.laa.2011.10.037〉. 〈hal-00926609〉

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