Error bounds for the perturbation of the Drazin inverse under some geometrical conditions |
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Authors: | J.Y. V lez-Cerrada, J. Robles,N. Castro-Gonz lez |
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Affiliation: | aFacultad de Informática, Universidad Politécnica de Madrid, 28660 Boadilla del Monte, Madrid, Spain |
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Abstract: | This paper studies the Drazin inverse for perturbed matrices. For that, given a square matrix A, we consider and characterize the class of matrices B with index s such that , and , where and denote the null space and the range space of a matrix A, respectively, and AD denote the Drazin inverse of A. Then, we provide explicit representations for BD and BBD, and upper bounds for the relative error BD-AD/AD and the error BBD-AAD. A numerical example illustrates that the obtained bounds are better than others given in the literature. |
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Keywords: | Singular matrix Drazin inverse Eigenprojectors Perturbation bounds |
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