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Full-rank representations of {2, 4}, {2, 3}-inverses and successive matrix squaring algorithm

We present the full-rank representations of {2, 4} and {2, 3}-inverses (with given rank as well as with prescribed range and null space) as particular cases of the full-rank representation of outer inverses. As a consequence, two applications of the successive matrix squaring (SMS) algorithm from [P...

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Bibliographic Details
Published in:Applied mathematics and computation 2011-07, Vol.217 (22), p.9358-9367
Main Authors: STANIMIROVIC, Predrag S, CVETKOVIC-ILIC, Dragana S, MILJKOVIC, Sladjana, MILADINOVIC, Marko
Format: Article
Language:English
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Summary:We present the full-rank representations of {2, 4} and {2, 3}-inverses (with given rank as well as with prescribed range and null space) as particular cases of the full-rank representation of outer inverses. As a consequence, two applications of the successive matrix squaring (SMS) algorithm from [P.S. Stanimirović, D.S. Cvetković-Ilić, Successive matrix squaring algorithm for computing outer inverses, Appl. Math. Comput. 203 (2008) 19–29] are defined using the full-rank representations of {2, 4} and {2, 3}-inverses. The first application is used to approximate {2, 4}-inverses. The second application, after appropriate modifications of the SMS iterative procedure, computes {2, 3}-inverses of a given matrix. Presented numerical examples clarify the purpose of the introduced methods.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.04.024