On splittings of matrices and nonnegative generalized inverses

Mishra, Debasisha; Sivakumar, K. C.

doi:10.7153/oam-06-06

Cited by 24 publications

(15 citation statements)

References 14 publications

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“…A method of construction of proper splitting can be found in [27] while its uniqueness is shown very recently in [28]. The result produced below is a combination of Theorem 5.2, [25] and Theorem 4.1, [27], and is also a special case of Theorem 3.2 & 3.3, [14] and Theorem 3.1, [33] when index 1 matrices are considered.…”

Section: Proper Splittingsmentioning

confidence: 93%

Three-step alternating iterations for index 1 and non-singular matrices

2019

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Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article, we introduce a new iteration scheme called three-step alternating iterations using proper splittings and group inverses to find an approximate solution of singular linear systems, iteratively. A preconditioned alternating iterative scheme is also proposed to relax some sufficient conditions and to obtain faster convergence as well. We then show that our scheme converges faster than the existing one. The theoretical findings are then validated numerically.

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Section: Proper Splittingsmentioning

confidence: 93%

Three-step alternating iterations for index 1 and non-singular matrices

2019

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“…Finally, convergence rate for both the splittings may be compared. Berman and Neumann [2] and Mishra and Sivakumar [20] obtained different methods of constructions for proper splittings. Hence the same case may be examined for the reverse proper splittings.…”

Section: Discussionmentioning

confidence: 99%

Reverse proper splittings of rectangular matrices

Mishra

2015

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“…3. A new type of splitting was introduced recently by Mishra and Sivakumar [15] with a view to study nonnegativity of the Moore-Penrose inverse and the group inverse. These are called B † -splitting and B # splitting.…”

Section: Discussionmentioning

confidence: 99%

Nonnegative generalized inverses in indefinite inner product spaces

Jayaraman

2013

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The aim of this article is to investigate nonnegativity of the inverse, the Moore-Penrose inverse and other generalized inverses, in the setting of indefinite inner product spaces with respect to the indefinite matrix product. We also propose and investigate generalizations of the corresponding notions of matrix monotonicity, namely, o-(rectangular) monotonicity, o-semimonotonicity and ?-weak monotonicity and its interplay with nonnegativity of various generalized inverses in the same setting.

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On splittings of matrices and nonnegative generalized inverses

Abstract: Abstract. The authors introduce a new type of matrix splitting generalizing the notion of Bsplitting and study its relationships with nonnegativity of the Moore-Penrose inverse and the group inverse.Mathematics subject classification (2010): 15A09, 15B48.

Cited by 24 publications

References 14 publications

Three-step alternating iterations for index 1 and non-singular matrices

Three-step alternating iterations for index 1 and non-singular matrices

Reverse proper splittings of rectangular matrices

Nonnegative generalized inverses in indefinite inner product spaces

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