General Six-Step Discrete-Time Zhang Neural Network for Time-Varying Tensor Absolute Value Equations
This article presents a general six-step discrete-time Zhang neural network (ZNN) for time-varying tensor absolute value equations. Firstly, based on the Taylor expansion theory, we derive a general Zhang et al. discretization (ZeaD) formula, i.e., a general Taylor-type 1-step-ahead numerical differ...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2019/4861912 |
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| author | Min Sun Jing Liu |
| author_facet | Min Sun Jing Liu |
| author_sort | Min Sun |
| collection | DOAJ |
| description | This article presents a general six-step discrete-time Zhang neural network (ZNN) for time-varying tensor absolute value equations. Firstly, based on the Taylor expansion theory, we derive a general Zhang et al. discretization (ZeaD) formula, i.e., a general Taylor-type 1-step-ahead numerical differentiation rule for the first-order derivative approximation, which contains two free parameters. Based on the bilinear transform and the Routh–Hurwitz stability criterion, the effective domain of the two free parameters is analyzed, which can ensure the convergence of the general ZeaD formula. Secondly, based on the general ZeaD formula, we design a general six-step discrete-time ZNN (DTZNN) for time-varying tensor absolute value equations (TVTAVEs), whose steady-state residual error changes in a higher order manner than those presented in the literature. Meanwhile, the feasible region of its step size, which determines its convergence, is also studied. Finally, experiment results corroborate that the general six-step DTZNN model is quite efficient for TVTAVE solving. |
| format | Article |
| id | doaj-art-e21ef283abcb40e79ec11fb196184917 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e21ef283abcb40e79ec11fb1961849172025-02-03T01:10:23ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2019-01-01201910.1155/2019/48619124861912General Six-Step Discrete-Time Zhang Neural Network for Time-Varying Tensor Absolute Value EquationsMin Sun0Jing Liu1School of Mathematics and Statistics, Zaozhuang University, Shandong, ChinaSchool of Data Sciences, Zhejiang University of Finance and Economics, Zhejiang, ChinaThis article presents a general six-step discrete-time Zhang neural network (ZNN) for time-varying tensor absolute value equations. Firstly, based on the Taylor expansion theory, we derive a general Zhang et al. discretization (ZeaD) formula, i.e., a general Taylor-type 1-step-ahead numerical differentiation rule for the first-order derivative approximation, which contains two free parameters. Based on the bilinear transform and the Routh–Hurwitz stability criterion, the effective domain of the two free parameters is analyzed, which can ensure the convergence of the general ZeaD formula. Secondly, based on the general ZeaD formula, we design a general six-step discrete-time ZNN (DTZNN) for time-varying tensor absolute value equations (TVTAVEs), whose steady-state residual error changes in a higher order manner than those presented in the literature. Meanwhile, the feasible region of its step size, which determines its convergence, is also studied. Finally, experiment results corroborate that the general six-step DTZNN model is quite efficient for TVTAVE solving.http://dx.doi.org/10.1155/2019/4861912 |
| spellingShingle | Min Sun Jing Liu General Six-Step Discrete-Time Zhang Neural Network for Time-Varying Tensor Absolute Value Equations Discrete Dynamics in Nature and Society |
| title | General Six-Step Discrete-Time Zhang Neural Network for Time-Varying Tensor Absolute Value Equations |
| title_full | General Six-Step Discrete-Time Zhang Neural Network for Time-Varying Tensor Absolute Value Equations |
| title_fullStr | General Six-Step Discrete-Time Zhang Neural Network for Time-Varying Tensor Absolute Value Equations |
| title_full_unstemmed | General Six-Step Discrete-Time Zhang Neural Network for Time-Varying Tensor Absolute Value Equations |
| title_short | General Six-Step Discrete-Time Zhang Neural Network for Time-Varying Tensor Absolute Value Equations |
| title_sort | general six step discrete time zhang neural network for time varying tensor absolute value equations |
| url | http://dx.doi.org/10.1155/2019/4861912 |
| work_keys_str_mv | AT minsun generalsixstepdiscretetimezhangneuralnetworkfortimevaryingtensorabsolutevalueequations AT jingliu generalsixstepdiscretetimezhangneuralnetworkfortimevaryingtensorabsolutevalueequations |