Recurrent Neural Network for Computing Outer Inverse

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

doi:10.1162/neco_a_00821

Cited by 32 publications

(6 citation statements)

References 31 publications

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“…The dynamic equation and induced gradient recurrent neural network for computing the Drazin inverse were defined in [24]. Two gradient-based RNNs for generating outer inverses with prescribed range and null space in the time-invariant case were introduced in [25]. Two additional dynamic state equations and corresponding gradient-based RNNs for generating the class of outer inverses of time-invariant real matrices were proposed in [26].…”

Section: Proposition 2 (Urquhart Formula) Let ∈ C 푚×푛 푟mentioning

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: Proposition 2 (Urquhart Formula) Let ∈ C 푚×푛 푟mentioning

confidence: 99%

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

et al. 2017

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“…In addition, we define a hybrid method which starts from the ZNN model (2.3) and finishes with (2.10). Finally, GNN denotes the gradient based neural network from [30] in the nonsingular case, corresponding to the case G = A T in the RNN1 model. The Simulink implementation of the ZNNNM model (2.3), restated in the equivalent forṁ…”

Section: Neural Network Architecturementioning

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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“…The study of generalized inverses of matrices has been a very important research field since the middle of last century and remains one of the most active research branches in the world [1][2][3]. Generalized inverses, including the weighted pseudoinverse, have numerous applications in various fields, such as control, networks, statistics, and econometrics [4][5][6][7]. The ℳℒ -weighted pseudoinverse of m × n matrix 𝒦 with the entries of two weight matrices ℳ and ℒ (with order s × m and l × n, respectively) is defined as…”

Section: Introductionmentioning

confidence: 99%

Conditioning Theory for ML-Weighted Pseudoinverse and ML-Weighted Least Squares Problem

Samar,

Zhu,

2024

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The conditioning theory of the ML-weighted least squares and ML-weighted pseudoinverse problems is explored in this article. We begin by introducing three types of condition numbers for the ML-weighted pseudoinverse problem: normwise, mixed, and componentwise, along with their explicit expressions. Utilizing the derivative of the ML-weighted pseudoinverse problem, we then provide explicit condition number expressions for the solution of the ML-weighted least squares problem. To ensure reliable estimation of these condition numbers, we employ the small-sample statistical condition estimation method for all three algorithms. The article concludes with numerical examples that highlight the results obtained.

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Recurrent Neural Network for Computing Outer Inverse

Cited by 32 publications

References 31 publications

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

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

ZNN models for computing matrix inverse based on hyperpower iterative methods

Conditioning Theory for ML-Weighted Pseudoinverse and ML-Weighted Least Squares Problem

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