Analytic perturbation of generalized inverses - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Linear Algebra and its Applications Year : 2013

Analytic perturbation of generalized inverses

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.
Fichier principal
Vignette du fichier
generinvlaa1.pdf (195.98 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

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

Identifiers

Cite

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⟩
148 View
398 Download

Altmetric

Share

Gmail Facebook X LinkedIn More