Perturbation bounds for $g$-inverses with respect to the unitarily invariant norm

Document Type: Research Paper

Author

College of Mathematics and Statistics‎, ‎Northwest Normal University‎, ‎Lanzhou 730070‎, ‎P.R‎. ‎China.

Abstract

Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest perturbed $g$-inverse. These results generalize and improve the existing results published recently to some extent.

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Main Subjects


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Volume 43, Issue 7
November and December 2017
Pages 2655-2662
  • Receive Date: 30 June 2017
  • Revise Date: 10 March 2018
  • Accept Date: 10 March 2018