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Article Dans Une Revue Linear Algebra and its Applications Année : 2013

Analytic perturbation of generalized inverses

Résumé

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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Dates et versions

hal-00926609 , version 1 (09-01-2014)

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Konstantin Avrachenkov, Jean-Bernard Lasserre. Analytic perturbation of generalized inverses. Linear Algebra and its Applications, 2013, 438 (4), pp.1793-1813. ⟨10.1016/j.laa.2011.10.037⟩. ⟨hal-00926609⟩
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