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Neural Comput. 2016 May;28(5):970-98. doi: 10.1162/NECO_a_00821. Epub 2016 Feb 18.

Recurrent Neural Network for Computing Outer Inverse.

Author information

1
Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11001 Beograd, Serbia zivkovic.ivan83@gmail.com.
2
University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, 18000 Niš, Serbia pecko@pmf.ni.ac.rs.
3
School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai, 200433, P.R.C. ymwei@fudan.edu.cn.

Abstract

Two linear recurrent neural networks for generating outer inverses with prescribed range and null space are defined. Each of the proposed recurrent neural networks is based on the matrix-valued differential equation, a generalization of dynamic equations proposed earlier for the nonsingular matrix inversion, the Moore-Penrose inversion, as well as the Drazin inversion, under the condition of zero initial state. The application of the first approach is conditioned by the properties of the spectrum of a certain matrix; the second approach eliminates this drawback, though at the cost of increasing the number of matrix operations. The cases corresponding to the most common generalized inverses are defined. The conditions that ensure stability of the proposed neural network are presented. Illustrative examples present the results of numerical simulations.

PMID:
26890345
DOI:
10.1162/NECO_a_00821

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