Full-rank representations of {2, 4}, {2, 3}-inverses and successive matrix squaring algorithm |
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Authors: | Predrag S Stanimirovi? Dragana S Cvetkovi?-Ili? Sladjana Miljkovi? Marko Miladinovi? |
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Institution: | University of Niš, Department of Mathematics, Faculty of Science, P.O. Box 224, Višegradska 33, 18000 Niš, Serbia |
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Abstract: | 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. Stanimirovi?, D.S. Cvetkovi?-Ili?, 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. |
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