Additive perturbation results for the Drazin inverse

By N. Gonzalez. 2005

57 citations recorded by the source corpus.

Abstract In this paper some new additive results for the Drazin inverse are presented. We give a formula for the Drazin inverse of a sum of two matrices under conditions on the matrices less restrictive than those imposed in the corresponding theorem given by Hartwig et al. (Linear Algebra Appl. 322 (2001) 207–217). We consider some aplications of our results to the perturbation of the Drazin inverse and analyze a number of special cases.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2240f5c554b458cb1bdd01c8a91486aee01d2b14

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In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Representations of the Drazin inverse on solution of a class singular differential equations (2011, background): “In 2005, Castro-González [6] gave a formula to calculate (AþB), where AB1⁄4 0, AB1⁄4 0 and B ABA 1⁄4 0, and in the same year Castro-González and Dopazo [7] gave the expression of the Drazin inverse for I I E 0 with E square.”
On the Drazin inverse of the sum of two operators and its application to operator matrices (2009, methodology): “Expressions of the Drazin inverse of the sum of two matrices under the weaker conditions AD B = AB D = 0 and (I − B B D)AB(I − A AD) = 0 were given in [4], and it was extended for elements in a Banach algebra in [6].”
A note on the representation for the Drazin inverse of 2×2 block matrices (2008, result): “First, we present an additive result for the Drazin inverse proved in [6], which we will be useful in proving our main result.”