2016
DOI: 10.1109/tcyb.2015.2479118
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Discontinuous Neural Networks for Finite-Time Solution of Time-Dependent Linear Equations

Abstract: This paper considers a class of nonsmooth neural networks with discontinuous hard-limiter (signum) neuron activations for solving time-dependent (TD) systems of algebraic linear equations (ALEs). The networks are defined by the subdifferential with respect to the state variables of an energy function given by the L norm of the error between the state and the TD-ALE solution. It is shown that when the penalty parameter exceeds a quantitatively estimated threshold the networks are able to reach in finite time, a… Show more

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Cited by 39 publications
(1 citation statement)
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“…Indeed, many papers have been written concerning applications of NNs to the above subject, see e.g. [27,6,42,35,32,38,36,31,28,34,29]. The main diculty arising in order to prove approximation results by means of NNs was to become able to construct concretely NNs which approximate a given function f dened on a xed bounded set of R s (s ∈ N + ).…”
Section: Introductionmentioning
confidence: 99%
“…Indeed, many papers have been written concerning applications of NNs to the above subject, see e.g. [27,6,42,35,32,38,36,31,28,34,29]. The main diculty arising in order to prove approximation results by means of NNs was to become able to construct concretely NNs which approximate a given function f dened on a xed bounded set of R s (s ∈ N + ).…”
Section: Introductionmentioning
confidence: 99%