Perturbation bounds of generalized inverses

Lingsheng Meng, Bing Zheng and Peilan Ma

Applied Mathematics and Computation, 2017, vol. 296, issue C, 88-100

Abstract: Let complex matrices A and B have the same sizes. We characterize the generalized inverse matrix B(1, i), called an {1, i}-inverse of B for each i=3 and 4, such that the distance between a given {1, i}-inverse of a matrix A and the set of all {1, i}-inverses of the matrix B reaches minimum under 2-norm (spectral norm) and Frobenius norm. Similar problems are also studied for {1, 2, i}-inverse. In practice, the matrix B is often considered as the perturbed matrix of A, and hence based on the previous results, the additive perturbation bounds for the {1, i}- and {1, 2, i}-inverses and multiplicative perturbation bounds for the {1}-, {1, i}- and {1, 2, i}-inverses are proposed. Numerical examples show that these multiplicative perturbation bounds can be achieved respective under 2-norm and Frobenius norm.

Keywords: Generalized inverses; Additive perturbation bound; Multiplicative perturbation bound; Distance; Optimality (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:296:y:2017:i:c:p:88-100

DOI: 10.1016/j.amc.2016.10.017

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