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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
first_indexed 2022-09-02T07:57:12Z
last_indexed 2023-01-13T19:21:33Z
id cronfa61008
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spelling 2022-10-07T11:22:14.8856376 v2 61008 2022-09-02 Towards Higher Order Dynamical Systems 42ff9eed09bcd109fbbe484a0f99a8a8 0000-0001-8316-5289 Shuai Li Shuai Li true false 2022-09-02 ACEM 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. Book chapter Generalized Inverses: Algorithms and Applications 207 240 Nova Science 978-168507356-5 978-168507513-2 1 1 2022 2022-01-01 https://novapublishers.com/shop/generalized-inverses-algorithms-and-applications/ https://novapublishers.com/shop/generalized-inverses-algorithms-and-applications/ COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University 2022-10-07T11:22:14.8856376 2022-09-02T08:53:49.9158689 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering Vasilios N. Katsikis 1 Predrag S. Stanimirovic 2 Spyridon D. Mourtas 3 Shuai Li 0000-0001-8316-5289 4 Xinwei Cao 5
title Towards Higher Order Dynamical Systems
spellingShingle Towards Higher Order Dynamical Systems
Shuai Li
title_short Towards Higher Order Dynamical Systems
title_full Towards Higher Order Dynamical Systems
title_fullStr Towards Higher Order Dynamical Systems
title_full_unstemmed Towards Higher Order Dynamical Systems
title_sort Towards Higher Order Dynamical Systems
author_id_str_mv 42ff9eed09bcd109fbbe484a0f99a8a8
author_id_fullname_str_mv 42ff9eed09bcd109fbbe484a0f99a8a8_***_Shuai Li
author Shuai Li
author2 Vasilios N. Katsikis
Predrag S. Stanimirovic
Spyridon D. Mourtas
Shuai Li
Xinwei Cao
format Book chapter
container_title Generalized Inverses: Algorithms and Applications
container_start_page 207
publishDate 2022
institution Swansea University
isbn 978-168507356-5
978-168507513-2
publisher Nova Science
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering
url https://novapublishers.com/shop/generalized-inverses-algorithms-and-applications/
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description 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.
published_date 2022-01-01T14:22:53Z
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score 11.543985

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