Recurrent Neural Network Approach Based on the Integral Representation of the Drazin Inverse-Reference-Cited by-同舟云学术

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

Published:2015-10 Issue:10 Volume:27 Page:2107-2131
ISSN:0899-7667
Container-title:Neural Computation
language:en
Short-container-title:Neural Computation

Author:

Stanimirović Predrag S.¹,Živković Ivan S.²,Wei Yimin³

Affiliation:

1. University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, 18000 Niš, Serbia

2. Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11001 Beograd, Serbia

3. School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai, 200433, China

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.

Publisher

MIT Press - Journals

Subject

Cognitive Neuroscience,Arts and Humanities (miscellaneous)

Link

https://www.mitpressjournals.org/doi/pdf/10.1162/NECO_a_00771

Reference38 articles.

1. Matrix Algebra

2. Ben-Israel, A. & Greville, T. N. E. (2003). Generalized inverses (2nd ed.). New York: Springer.

3. Generalized Inverses of Linear Transformations

4. Applications of the Drazin Inverse to Linear Systems of Differential Equations with Singular Constant Coefficients

5. Unified stabilization approach to principal and minor components extraction algorithms

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