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Towards Higher Order Dynamical Systems

Vasilios N. Katsikis, Predrag S. Stanimirovic, Spyridon D. Mourtas, Shuai Li Orcid Logo, Xinwei Cao

Generalized Inverses: Algorithms and Applications, Pages: 207 - 240

Swansea University Author: Shuai Li Orcid Logo

Abstract

Hyperpower family of iterative methods of arbitrary convergence order is one of the most frequently applied methods for approximating the matrix inverse and generalized inverses. On the other hand, Zeroing neural network (ZNN) is a kind of neural dynamics designed for solving time-varying problems....

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Published in: Generalized Inverses: Algorithms and Applications
ISBN: 978-168507356-5 978-168507513-2
Published: Nova Science 2022
Online Access: https://novapublishers.com/shop/generalized-inverses-algorithms-and-applications/
URI: https://cronfa.swan.ac.uk/Record/cronfa61008
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Abstract: Hyperpower family of iterative methods of arbitrary convergence order is one of the most frequently applied methods for approximating the matrix inverse and generalized inverses. On the other hand, Zeroing neural network (ZNN) is a kind of neural dynamics designed for solving time-varying problems. This research is aimed to study the analogy between the scaled hyperpower iterative family (SHPI family) for computing the matrix inverse and the discretized Zhang Neural Network (DZNN) models. On the basis of the discovered analogy, a family of ZNN models corresponding to the hyperpower iterative methods is defined. These models are termed as higher-order ZNN models (HOZNN) and are applicable in computing the matrix pseudoinverse. In addition, integration-enhanced and noise-handling HOZNN class of dynamical systems, termed as IENHZNN, is introduced. Theoretical and numerical comparisons between the standard ZNN and HOZNN dynamic flows are considered.
Item Description: https://novapublishers.com/shop/generalized-inverses-algorithms-and-applications/
College: College of Engineering
Start Page: 207
End Page: 240