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2015•Neural ComputationRequires access

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

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

Open publisher page 56 citations

Abstract

In this letter, we present the dynamical equation and corresponding artificial recurrent neural network for computing the Drazin inverse for arbitrary square real matrix, without any restriction on its eigenvalues. Conditions that ensure the stability of the defined recurrent neural network as well as its convergence toward the Drazin inverse are considered. Several illustrative examples present the results of computer simulations.

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What this paper is about

In this letter, we present the dynamical equation and corresponding artificial recurrent neural network for computing the Drazin inverse for arbitrary square real matrix, without any restriction on its eigenvalues. Conditions that ensure the stability of the defined recurrent neural network as well as its convergence toward the Drazin inverse are considered. Several illustrative examples present the results of computer simulations.

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OpenAlex reports 56 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this letter, we present the dynamical equation and corresponding artificial recurrent neural network for computing the Drazin inverse for arbitrary square real matrix, without any restriction on its eigenvalues. Conditions that ensure the stability of the defined recurrent neural network as well as its convergence toward the Drazin inverse are considered. Several illustrative examples present the results of computer simulations.

Key concepts: Drazin inverse, Artificial neural network, Eigenvalues and eigenvectors, Mathematics, Inverse, Convergence (economics), Matrix (chemical analysis), Stability (learning theory)

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