Discrete Model Solving Time-Dependent Matrix Eigen Problem with ZeaD (Zhang et al Discretization) Formula Using 7 Points

Zhang, Yunong; Li, Chu-Min; Li, Jian; Wu, Guohui; Huang, Huanchang

doi:10.23919/chicc.2018.8483264

Cited by 5 publications

(5 citation statements)

References 16 publications

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“…en, the le -hand sides of the inequalities in (23) are 16/105, 142/105, 104/71, 4762/1365, 3835/553, and 2, respectively, which indicate that 1 = −1/20 and 2 = 47/420 satisfy this system. us, the six-step fourth-order ZeaD formula [20] is convergent. Dropping the term 4 on the right-hand side of (21), we de ne a computable general six-step DTZNN model where ( = 1, 2, .…”

Section: Proofmentioning

confidence: 95%

“…, 6) are the coe cients of (51). When 1 = −1/20 and 2 = 47/420, we get the following concrete model: [20] . For this case, by eorem 17, we get the e ective domain of ℎ is which is the same as that given in [20].…”

Section: The General Six-step Fourth-order Zead Formulamentioning

confidence: 99%

“…When 1 = −1/20 and 2 = 47/420, we get the following concrete model: [20] . For this case, by eorem 17, we get the e ective domain of ℎ is which is the same as that given in [20]. (62) 11 > 0, 12 > 0, 13 > 0, 14 > 0, 21 > 0, 23 > 0, 31 > 0, 41 > 0, 51 > 0, 61 > 0,…”

Section: The General Six-step Fourth-order Zead Formulamentioning

confidence: 99%

“…Solving this model, we get the optimal step length ℎ * = 0.1359. If we set the objective function as max ᐈ ᐈ ᐈ ᐈ ᐈ ᐈ ᐈ ᐈ , the optimal step length ℎ * = 0.1158, the same as that in [20].…”

Section: Example 19 Consider the Following Time-invariant Tensor Valmentioning

confidence: 99%

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General Six-Step Discrete-Time Zhang Neural Network for Time-Varying Tensor Absolute Value Equations

Sun

Liu

2019

Discrete Dynamics in Nature and Society

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is 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 di erentiation rule for the rst-order derivative approximation, which contains two free parameters. Based on the bilinear transform and the Routh-Hurwitz stability criterion, the e ective 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 e cient for TVTAVE solving.

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Section: Proofmentioning

confidence: 95%

Section: The General Six-step Fourth-order Zead Formulamentioning

confidence: 99%

Section: The General Six-step Fourth-order Zead Formulamentioning

confidence: 99%

Section: Example 19 Consider the Following Time-invariant Tensor Valmentioning

confidence: 99%

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General Six-Step Discrete-Time Zhang Neural Network for Time-Varying Tensor Absolute Value Equations

Sun

Liu

2019

Discrete Dynamics in Nature and Society

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“…Third one is MTCNN [9] or Multi-Task Cascaded Convolutional Neural Networks is a neural network which detects faces and facial landmarks on images. It was published in 2016 by Zhang et al [10]. It is one of the most popular and most accurate face detection tools today.…”

Section: Tools For Face Detecting For Todaymentioning

confidence: 99%

Comparision of Face Detection Tools

Amirgaliyev¹,

Садыкова

Kenshimov

2021

Bullet. Ser. of Phys. & Math. Sc.

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This article examines the assessment of tools such as Dlib, OpenCV, MTCNN, FaceNet for face recognition. In the process of work, the execution time and the count of detecting of each tool were determined and calculated. The results pictured in graph choose the right tool according to the data obtained in the article that was optimal for next research works. The choice was made for the ease of writing a parallel algorithm. The rationale for the choice of the tool is also given according to the parameters of the use of machine resources, which makes it possible to optimally select a machine without additional and large costs. A comparative analysis of each instrument was performed and the results were identified accordingly. Based on the test results, we divided two cases and tried to give recommendations for each of them. The first case is triggered if only quick face detection is considered in the video. The second case is triggered if more faces are viewed in the video. It turned out that in the first case, we need to use the Dlib tool. In the second case, we can choose tools like Facenet or Mtcnn. The results obtained in the process of the research are presented in the form of graphs, tables and recorded in the conclusion section of this article.

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No 8-Instant ZTD (Zhang Time Discretization) Formula with Quintic Precision or Higher as Proved

Zhang

Zheng

2021

2021 China Automation Congress (CAC)

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Discrete Model Solving Time-Dependent Matrix Eigen Problem with ZeaD (Zhang et al Discretization) Formula Using 7 Points

Cited by 5 publications

References 16 publications

General Six-Step Discrete-Time Zhang Neural Network for Time-Varying Tensor Absolute Value Equations

General Six-Step Discrete-Time Zhang Neural Network for Time-Varying Tensor Absolute Value Equations

Comparision of Face Detection Tools

No 8-Instant ZTD (Zhang Time Discretization) Formula with Quintic Precision or Higher as Proved

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