Global-DGMRES method for matrix equation<i>AXB</i> = <i>C</i>

Safarzadeh, Malihe; Goughery, Hossein Sadeghi; Salemi, Abbas

doi:10.1080/00207160.2021.1942459

Cited by 2 publications

(5 citation statements)

References 24 publications

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“…On the other hand, the residual error of the IEZNN model ( 5) and the IEAZNN model ( 10) can achieve convergence but the residual convergence speed and convergence accuracy of the IEZNN model ( 5) are not as good as those of the IEAZNN model (10). For example, when γ 1 = γ 2 = 1, the residual error convergence accuracy of the IEAZNN model ( 10) can reach the 10 −2 level, which is better than the 10 −1 of the IEZNN model (5). As shown in Figure 3c,d, although the residual error of the traditional CZNN model (3) still cannot be reduced to 0, the increase is smaller than that of the case when γ 1 = 1.…”

Section: Comparative Verificationsmentioning

confidence: 98%

“…X(t) ∈ R m×n is the time-varying unknown matrix that we need to solve in real time to satisfy the time-varying problem (1). The problem (1) solving is widely applied to many practical problems in control theory and has been mentioned in many papers [5,29,30].…”

Section: Problem Formulation and Related Modelsmentioning

confidence: 99%

“…In the application of image blurring, we consider the time-invariant special case of LME (1). A and B represent a 100 × 100-dimensional Toeplitz matrix [5], which is constructed by formula (23) and A = B. X represents the original image, and C represents the blurred image. We consider r = 8.…”

Section: Comparative Verificationsmentioning

confidence: 99%

“…The advances in computer science have extended its use in various fields of application, such as the robotics domain [1-3], adaptive neural tracking control [4] and imageprocessing [5]. Among all the applications mentioned above, the linear matrix equation (LME) is one of the most commonly seen problems.…”

Section: Introductionmentioning

confidence: 99%

“…Comparison of solving accuracies of the CZNN model (3), IEZNN model(5) and IEAZNN model(10) under different noise and design parameters.…”

mentioning

confidence: 99%

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Zeroing Neural Networks Combined with Gradient for Solving Time-Varying Linear Matrix Equations in Finite Time with Noise Resistance

et al. 2022

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Due to the time delay and some unavoidable noise factors, obtaining a real-time solution of dynamic time-varying linear matrix equation (LME) problems is of great importance in the scientific and engineering fields. In this paper, based on the philosophy of zeroing neural networks (ZNN), we propose an integration-enhanced combined accelerating zeroing neural network (IEAZNN) model to solve LME problem accurately and efficiently. Different from most of the existing ZNNs research, there are two error functions combined in the IEAZNN model, among which the gradient of the energy function is the first design for the purpose of decreasing the norm-based error to zero and the second one is adding an integral term to resist additive noise. On the strength of novel combination in two error functions, the IEAZNN model is capable of converging in finite time and resisting noise at the same time. Moreover, theoretical proof and numerical verification results show that the IEAZNN model can achieve high accuracy and fast convergence speed in solving time-varying LME problems compared with the conventional ZNN (CZNN) and integration-enhanced ZNN (IEZNN) models, even in various kinds of noise environments.

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Section: Comparative Verificationsmentioning

confidence: 98%

Section: Problem Formulation and Related Modelsmentioning

confidence: 99%