GMDS-ZNN Model 3 and its Ten-Instant Discrete Algorithm for Time-Variant Matrix Inversion Compared With Other Multiple-Instant Ones

Wu, Dongqing; Zhang, Yunong; Li, Zhenyu; Ming, Liangjie

doi:10.1109/access.2020.3045780

Cited by 12 publications

(5 citation statements)

References 31 publications

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“…where c 0 � 100/237, c [25]. With (10) and ( 32), the teninstant ZMMMI algorithm is named as ZMMMI10i algorithm, which is thus obtained:…”

Section: 24mentioning

confidence: 99%

“…A(t) ∈ R n×n of full rank. With sufficiently small sampling gap ϵ ∈ (0, 1), the maximal steady-state residual error lim k⟶+∞ sup‖A k+1 X k+1 A k+1 − A k+1 ‖ F of discrete algorithm (25), ( 27), ( 29), (31), or (33) is O(ϵ p ), where p � 2, 3, 4, 5 or 6.…”

Section: Theorem 1 Consider a Smoothly Time-variant Real Matrixmentioning

confidence: 99%

“…According to (25), ( 27), ( 29), (31), and (33), we have X k+1 � B k+1 + O(ϵ p ), with ϵ ∈ (0, 1), and further have…”

Section: Theorem 1 Consider a Smoothly Time-variant Real Matrixmentioning

confidence: 99%

“…e results of the numerical experiments for ZMMMI2i algorithm (25), ZMMMI4i algorithm (27), ZMMMI6i algorithm (29), ZMMMI8i algorithm (31), and ZMMMI10i algorithm (33) are shown in Figures 7 and 8. e experimental results are satisfactory as expected.…”

Section: Zmmmi Modelmentioning

confidence: 99%

“…In theoretical and practical researches, the ZNN models claim their natural advantages in convergence and high accuracy. Inspired by this idea, the ZFs have been found to speed up and consolidate the development of various ZNN models [20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

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The time-variant matrix inversion (TVMI) problem solving is the hotspot of current research because of its frequent appearance and application in scientific research and industrial production. The generalized inverse problem of singular square matrix and nonsquare matrix can be related to Penrose equations (PEs). The PEs implicitly define the generalized inverse of a known matrix, which is of fundamental theoretical significance. Therefore, the in-depth study of PEs might enlighten problem solving of TVMI in a foreseeable way. For the first time, we construct three different matrix error-monitoring functions based on PEs and propose the corresponding models for TVMI problem solving by using the substitution technique and ZNN design formula. In order to facilitate computer simulation, the obtained continuous-time models are discretized by using ZTD (Zhang time discretization) formulas. Furthermore, the feasibility and effectiveness of the novel Zhang neural network (ZNN) multiple-multiplication model for matrix inverse (ZMMMI) and the PEs-based Getz–Marsden dynamic system (PGMDS) model in solving the problem of TVMI are investigated and shown via theoretical derivation and computer simulation. Computer experiment results also illustrate that the direct derivative dynamics model for TVMI is less effective and feasible.

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“…where c 0 � 100/237, c [25]. With (10) and ( 32), the teninstant ZMMMI algorithm is named as ZMMMI10i algorithm, which is thus obtained:…”

Section: 24mentioning

confidence: 99%

Section: Theorem 1 Consider a Smoothly Time-variant Real Matrixmentioning

confidence: 99%

“…According to (25), ( 27), ( 29), (31), and (33), we have X k+1 � B k+1 + O(ϵ p ), with ϵ ∈ (0, 1), and further have…”

Section: Theorem 1 Consider a Smoothly Time-variant Real Matrixmentioning

confidence: 99%

Section: Zmmmi Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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GMDS-ZNN Model 3 and its Ten-Instant Discrete Algorithm for Time-Variant Matrix Inversion Compared With Other Multiple-Instant Ones

Cited by 12 publications

References 31 publications

From Penrose Equations to Zhang Neural Network, Getz–Marsden Dynamic System, and DDD (Direct Derivative Dynamics) Using Substitution Technique

From Penrose Equations to Zhang Neural Network, Getz–Marsden Dynamic System, and DDD (Direct Derivative Dynamics) Using Substitution Technique

Simplified GZN (Gradient-Zhang Neurodynamic) Continuous-Model and Discrete-Algorithms Handling Temporally-Varying ODLMVE (Over-Determined Linear Matrix-Vector Equation)

Theoretical Analysis of Gradient-Zhang Neural Network for Time-Varying Equations and Improved Method for Linear Equations

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