Recurrent Neural Network Approach Based on the Integral Representation of the Drazin Inverse

Stanimirović, Predrag S.; Živković, Ivan S.; Wei, Yimin

doi:10.1162/neco_a_00771

Cited by 46 publications

(12 citation statements)

References 30 publications

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“…Remark 1: The convergence of neural network systems (9), (11) and 13is adjusted by parameters ξ and η. And γ is the parameter of sign-bi-power function (8).…”

Section: Design Of Cvsznn Modelmentioning

confidence: 99%

Comprehensive Analysis of ZNN Models for Computing Complex-Valued Time-Dependent Matrix Inverse

2020

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Computing complex-valued time-dependent matrix inverse is an important procedure in statistics and control theory. Zeroing neural network (ZNN) becomes an effective method for solving timedependent issues. This paper proposes a complex-valued synthetical ZNN (CVSZNN) model for computing complex-valued time-dependent matrix inverse within different noise environments. Two important property is synthetically dissected in the construction process of CVSZNN model. First, the finite-time convergence, to ensure the efficiency of CVSZNN model for solving complex-valued time-dependent issue. Secondly, the anti-noise property, to guarantee the robustness of CVSZNN model in presence of noises. Two important aspects above have been validated by theoretical analysis and numerical experiments. Furthermore, the impact of parameters values is investigated based on the experimental results. As compared with the existing ZNN models for computing complex-valued time-dependent matrix inverse, the superiority of the proposed CVSZNN model is displayed fully. INDEX TERMS Zeroing neural network, time-dependent, finite-time convergence, complex-valued, antinoise, matrix inverse.

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“…Remark 1: The convergence of neural network systems (9), (11) and 13is adjusted by parameters ξ and η. And γ is the parameter of sign-bi-power function (8).…”

Section: Design Of Cvsznn Modelmentioning

confidence: 99%

Comprehensive Analysis of ZNN Models for Computing Complex-Valued Time-Dependent Matrix Inverse

2020

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“…The model (28) is aimed to computation of v j . Finally, the complex ZNN model (28) initiates the (ij)th neuron s dynamic equation in the form (29) Clearly, values of λ closer to zero lead to better approximation of the limiting representation (9).…”

Section: The Znnwipi Modelsmentioning

confidence: 99%

“…The relationship between the Zhang matrix inverse and the Drazin inverse, discovered in [45], leads to the same dynamic state equation which was considered in [30] in the time invariant matrix case. The dynamical equation and corresponding artificial recurrent neural network for computing the Drazin inverse of an arbitrary square real matrix, without any restriction on eigenvalues of its rank invariant powers, were proposed in [29]. Zhang et all.…”

Section: Introductionmentioning

confidence: 99%

Complex ZNN for computing time-varying weighted pseudo-inverses

Stanimirović

Wang

2019

APPL ANAL DISCRETE M

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We classify, extend and unify various generalizations of weighted Moore-Penrose inverses in indefinite inner product spaces. New kinds of generalized inverses are introduced for this purpose. These generalized inverses are included in the more general class called as the weighted indefinite pseudoinverses (WIPI), which represents an extension of the Minkowski inverse (MI), the weighted Minkowski inverse (WMI), and the generalized weighted Moore-Penrose (GWM-P) inverse. The WIPI generalized inverses are introduced on the basis of two Hermitian invertible matrices and two Hermitian involuntary matrices and represented as particular outer inverses with prescribed ranges and null spaces, in terms of appropriate full-rank and limiting representations. Application of introduced generalized inverses in solving some indefinite least squares problems is considered. New Zeroing Neural Network (ZNN) models for computing the WIPI are developed using derived full-rank and limiting representations. The convergence behavior of the proposed ZNN models is investigated. Numerical simulation results are presented.

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“…The relationship between the Zhang matrix inverse and the Drazin inverse, discovered in [25], leads to the same dynamic state equation which was considered in [17] in the time invariant matrix case. The dynamical equation and corresponding artificial recurrent neural network for computing the Drazin inverse of an arbitrary square real matrix, without any restriction on eigenvalues of its rank invariant powers, were proposed in [16]. A discrete-time model of ZNN for matrix inversion, which is depicted by a system of difference equations, was investigated in [27].…”

Section: Introductionmentioning

confidence: 99%

ZNN models for computing matrix inverse based on hyperpower iterative methods

Stojanović

Stanimirović

Zivkovic

et al. 2017

Filomat

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Abstract. Our goal is to investigate and exploit an analogy between the scaled hyperpower family (SHPI family) of iterative methods for computing the matrix inverse and the discretization of Zhang Neural Network (ZNN) models. A class of ZNN models corresponding to the family of hyperpower iterative methods for computing generalized inverses is defined on the basis of the discovered analogy. The Simulink implementation in Matlab of the introduced ZNN models is described in the case of scaled hyperpower methods of the order 2 and 3. Convergence properties of the proposed ZNN models are investigated as well as their numerical behavior.

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Recurrent Neural Network Approach Based on the Integral Representation of the Drazin Inverse

Cited by 46 publications

References 30 publications

Comprehensive Analysis of ZNN Models for Computing Complex-Valued Time-Dependent Matrix Inverse

Comprehensive Analysis of ZNN Models for Computing Complex-Valued Time-Dependent Matrix Inverse

Complex ZNN for computing time-varying weighted pseudo-inverses

ZNN models for computing matrix inverse based on hyperpower iterative methods

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