Recurrent neural network for computing the W-weighted Drazin inverse

Wang, Xuezhong; Ma, Haifeng; Stanimirović, Predrag S.

doi:10.1016/j.amc.2016.11.030

Cited by 22 publications

(3 citation statements)

References 45 publications

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“…This definition does not have flexibility in the rings and semi-groups of associations but commutes with the element. The importance of this type of inverse and its calculation was later discussed by Wilkinson [10], and several researchers proposed direct or iterative methods for calculating the solution of this problem [11][12][13][14]. In this paper, a characterization of the Drazin inverse in the scope of fractional calculus is investigated.…”

Section: Introductionmentioning

confidence: 99%

On the Calculation of the Moore–Penrose and Drazin Inverses: Application to Fractional Calculus

et al. 2021

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This paper presents a third order iterative method for obtaining the Moore–Penrose and Drazin inverses with a computational cost of O(n3), where n∈N. The performance of the new approach is compared with other methods discussed in the literature. The results show that the algorithm is remarkably efficient and accurate. Furthermore, sufficient criteria in the fractional sense are presented, both for smooth and non-smooth solutions. The fractional elliptic Poisson and fractional sub-diffusion equations in the Caputo sense are considered as prototype examples. The results can be extended to other scientific areas involving numerical linear algebra.

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Section: Introductionmentioning

confidence: 99%

On the Calculation of the Moore–Penrose and Drazin Inverses: Application to Fractional Calculus

et al. 2021

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“…The Drazin inverse is very useful, and its applications in automatics, probability, statistics, mathematical programming, numerical analysis, game theory, econometrics, control theory and so on, can be found in [2,3]. For more recent results related to generalized Drazin inverse, W-weighted Drazin inverse and Drazin inverse see [16,19,20,21].…”

Section: Introductionmentioning

confidence: 99%

The gDMP inverse of Hilbert space operators

Mosić

Djordjević

2018

J. Spectr. Theory

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We present the weighted weak group inverse, which is a new generalized inverse of operators between two Hilbert spaces, introduced to extend weak group inverse for square matrices. Some characterizations and representations of the weighted weak group inverse are investigated. We also apply these results to define and study the weak group inverse for a Hilbert space operator. Using the weak group inverse, we define and characterize various binary relations.

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“…Se puede decir que esta extensión es uno de los primeros antecedentes en el intento de extender una inversa generalizada para matrices cuadradas al caso rectangular. A partir de la inversa de Drazin ponderada surgieron numerosos trabajos de investigación tanto en sus aspectos teóricos como así también en sus aplicaciones [26, 28,30,32,33,52,56,60,61]. Siguiendo una técnica similar, en 2017, Meng [38] denió la inversa DMP para matrices rectangulares, llamada inversa DMP ponderada.…”

Section: Introductionunclassified

La inversa core-EP y la inversa de grupo débil para matrices rectangulares

Orquera¹

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Generalized inverses, known today as Classical Generalized Inverses, were studied during the rst decades of the last century. Two important classical generalized inverses are the Moore-Penrose inverse (1955) and the Drazin inverse (1958). The Moore-Penrose inverse was originally dened for complex rectangular matrices. In turn, the Drazin inverse was studied, at rst, only for square matrices. It was in 1980 when Cline and Greville extended the case of square matrices to the case of rectangular matrices by considering a weight rectangular matrix. Throughout the entire past century there appeared dierent properties, characterizations and applications of these types of generalized inverses.This last decade gave rise to new notions of generalized inverses. The rst of these new notions is known as the core inverse. Core inverses were introduced in 2010 by Baksalary and Trenkler. Their work had a wide repercussion in the mathematical community due to the simplicity of its denition and its application in the solution of some linear systems with restrictions. The core inverse further gain in interest due to their connection to the Bott-Dun inverse. There is a large body of work on the core inverse, including extensions to more general sets such as the algebra of bounded linear operators on Hilbert spaces and/or abstract rings. v

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Recurrent neural network for computing the W-weighted Drazin inverse

Cited by 22 publications

References 45 publications

On the Calculation of the Moore–Penrose and Drazin Inverses: Application to Fractional Calculus

On the Calculation of the Moore–Penrose and Drazin Inverses: Application to Fractional Calculus

The gDMP inverse of Hilbert space operators

La inversa core-EP y la inversa de grupo débil para matrices rectangulares

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