A method for solving the system of linear equations and linear inequalities

Pang, Li-Ping; Spedicato, Emilio; Xia, Zhixun; Wang, Wei

doi:10.1016/j.mcm.2006.12.007

Cited by 14 publications

(34 citation statements)

References 7 publications

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“…For more details of the ABS class we refer the interested reader to [1,2,6,13]. In this paper we use the IGC algorithm (see the Appendix A) of the ABS class to solve the following linear system:…”

Section: A Methods For Minimizing the Operationsmentioning

confidence: 99%

Solving fully fuzzy linear systems by using implicit Gauss–Cholesky algorithm

Abbasbandy

Hashemi

2012

Comput Math Model

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Section: A Methods For Minimizing the Operationsmentioning

confidence: 99%

Solving fully fuzzy linear systems by using implicit Gauss–Cholesky algorithm

Abbasbandy

Hashemi

2012

Comput Math Model

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“…Concretely, Q is the m by q matrix with Q 1 , ...,Q q as columns. For a method of solving of the system of linear inequalities see [11].…”

Section: Lypunov Functions Of Sqso (25)mentioning

confidence: 99%

Separable quadratic stochastic operators

Rozikov

Nazir

2010

Lobachevskii J Math

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We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well-known, we mainly study properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. Also we compare our results with known results of the theory of quadratic operators and give some open problems.

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“…Solving such a LEI problem is essentially finding simultane-ous solutions that satisfy equation and inequality. Obviously, the LEI problem has a great importance in the variant application, it becomes necessary and meaningful to develop an effective unified solution scheme [11]- [13]. Currently, a lot of studies have been proposed which aim at solving the LEI problem.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, Liang et al [18] utilize the discrete-time zeroing neural network to solve the LEI problem and give the corresponding improved upper limit of the step size parameters. However, it is worth noting (11) Yes Yes Yes Yes Negligible Negligible BS † BS † Note that the recurrent neural network in [17] is constructed to solve the static LEI problem. NA means that the item cannot be obtained from the algorithm in the corresponding papers.…”

Section: Introductionmentioning

confidence: 99%

Solving Perturbed Time-Varying Linear Equation and Inequality Problem With Adaptive Enhanced and Noise Suppressing Zeroing Neural Network

Huang

et al. 2022

IEEE Access

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Solving time-varying linear equation and inequality (TVLEI) problem has attracted extensive attention in numerous scientific and engineered fields. In this article, it is basically considered that the commonly used dynamics neural network in the virtual environment is inevitably interfered with by the variable measurement noises while dealing with the TVLEI problem. An adaptive enhanced and noisesuppressing zeroing neural network (AENSZNN) model is proposed as an improved algorithm for solving the TVLEI problem. An adaptive scale factor based on the residual error norm is designed to make the proposed AENSZNN model converge to the theoretical solution faster. Furthermore, the momentum enhancement terms added to the model enables the AENSZNN model to effectively solve the TVLEI problem in real-time under the obstruction of different measurement noises. Besides, theoretical results and numerical experiments indicate that the AENSZNN model has advantages in convergence accuracy and robustness to noises compared with the existing algorithms. Note that, the proposed AENSZNN model is successfully exploited for the estimation of mobile object localization.

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A method for solving the system of linear equations and linear inequalities

Cited by 14 publications

References 7 publications

Solving fully fuzzy linear systems by using implicit Gauss–Cholesky algorithm

Solving fully fuzzy linear systems by using implicit Gauss–Cholesky algorithm

Separable quadratic stochastic operators

Solving Perturbed Time-Varying Linear Equation and Inequality Problem With Adaptive Enhanced and Noise Suppressing Zeroing Neural Network

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