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

Stanimirović, Predrag S.; Cvetković-Ilić, Dragana S.; Miljković, Sladjana; Miladinović, Marko

doi:10.1016/j.amc.2011.04.024

Cited by 16 publications

(25 citation statements)

References 17 publications

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“…(g) Theorem 6 and the full-rank representation of {2, 4}-and {2, 3}-inverses from [30] are a theoretical basis for computing {2, 4}-and {2, 3}-inverses with the prescribed range and null space.…”

Section: Complexity Of Algorithmsmentioning

confidence: 99%

Conditions for Existence, Representations, and Computation of Matrix Generalized Inverses

et al. 2017

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Conditions for the existence and representations of {2}-, {1}-, and {1, 2}-inverses which satisfy certain conditions on ranges and/or null spaces are introduced. These representations are applicable to complex matrices and involve solutions of certain matrix equations. Algorithms arising from the introduced representations are developed. Particularly, these algorithms can be used to compute the Moore-Penrose inverse, the Drazin inverse, and the usual matrix inverse. The implementation of introduced algorithms is defined on the set of real matrices and it is based on the Simulink implementation of GNN models for solving the involved matrix equations. In this way, we develop computational procedures which generate various classes of inner and outer generalized inverses on the basis of resolving certain matrix equations. As a consequence, some new relationships between the problem of solving matrix equations and the problem of numerical computation of generalized inverses are established. Theoretical results are applicable to complex matrices and the developed algorithms are applicable to both the time-varying and time-invariant real matrices.

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Section: Complexity Of Algorithmsmentioning

confidence: 99%

Conditions for Existence, Representations, and Computation of Matrix Generalized Inverses

et al. 2017

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“…We extend the results given in [20,23] to the case of indefinite inner product. Also, some new representations of generalized inverses are derived and extend to the case of indefinite inner product.…”

Section: ð1:3þmentioning

confidence: 84%

“…The existence and representations of some classes of generalized inverses, including A ð2Þ T;Ã and A ð2Þ Ã;S were given in [8]. Iterative schemes for numerical computation of f2; 3g and f2; 4g-inverses were developed in [22,23]. Authors of the paper [23] derived full-rank representations of f2; 3g and f2; 4g generalized inverses with prescribed range and null space as particular cases of the full-rank representation of generalized inverses A ð2Þ T;S , which is established in [19].…”

Section: ð1:3þmentioning

confidence: 99%

“…It provides a uniform generalization of all known algorithms for their calculation. Our choice is to define a generalization of the SMS iterative algorithm from [23]. Namely, the SMS algorithm in [23] is aimed in computation of f2; 3g and f2; 4g-inverses with prescribed range and null space for the set of complex matrices.…”

Section: ð1:3þmentioning

confidence: 99%

“…Iterative schemes for numerical computation of f2; 3g and f2; 4g-inverses were developed in [22,23]. Authors of the paper [23] derived full-rank representations of f2; 3g and f2; 4g generalized inverses with prescribed range and null space as particular cases of the full-rank representation of generalized inverses A ð2Þ T;S , which is established in [19]. Introduced full-rank representations enable adaptation of the well-known algorithms for computing outer inverses with prescribed range and null space into corresponding algorithms for computing f2; 3g and f2; 4g-inverses.…”

Section: ð1:3þmentioning

confidence: 99%

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