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International Conference on Intelligent and Fuzzy Systems (INFUS)

作者： Petunin, Aleksandr Ukolov, Stanislav Ural Fed Univ 19 Mira St Ekaterinburg 620002 Russia IMM UB Ras 16 S Kovalevskaya St Ekaterinburg 620108 Russia

ISBN: (纸本)9783031671944;9783031671951

The paper proposes a new algorithm for solving one class of the tool path problems for CNC sheet cutting machines (the generalized segmental continuous cutting problem, GSCCP) with an additional parameter limited the calculation time for finding an optimal solution. As input data in the GSCCP, 2D layout of nested parts and a finite set of subtasks for optimizing the cutting path are used. Each subtask contains a set of so-called basic cutting segments, which determine the trajectories of tool movement between the points for material piercing and the points for switching tool off. Each subtask can be solved independently within the specified calculation time. The best solution found for the all subtasks is a solution to the GSCCP problem. The proposed iterative algorithm involves quantizing the total computation time. Moreover, within each time quant, all subtasks are also solved sequentially by calculation the upper and lower bounds. Initial upper bounds can, for example, be obtained using any fast heuristic based on effective combinatorial optimization methods. Next, for each of them, the procedure for searching for the lower boundary is launched. The next iteration of the solution process is performed taking into account the adjusted bounds. The solution procedures are interrupted when the specified time quant is reached, or upon obtaining a guaranteed exact solution. The effectiveness of the algorithm is illustrated by practical examples. It is also shown that for generate a set of finite set of subtasks for GSCCP, it is advisable to use neural networks.

关键词： Cutting path Tool Path Problem Segment Cutting Optimization time iterative algorithm Time Quantizing Lower and upper bounds Classification Problem

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Generating non-Gaussian rough surfaces using analytical functions and spectral representation method with an iterative algorithm

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APPLIED MATHEMATICAL MODELLING 2025年第PartA期137卷

作者： Chen, Jian Zang, Fuquan Zhao, Xiaohui Li, Hou Tong, Zeteng Yuan, Kening Zhu, Linbo Xian Polytech Univ Sch Mech & Elect Engn Xian 710048 Peoples R China Xi An Jiao Tong Univ Sch Chem Engn & Technol Xian 710049 Peoples R China

The non-Gaussian rough surface simulation method with desired spatial distribution and height distribution is generally used to analyse the contact characteristics of rough surfaces under different contact conditions. Conventional surface simulation methods have disadvantages in terms of their range, accuracy, and stability. In this study, the analytical function method is enhanced to generate non-Gaussian random number matrices. The enhanced method was combined with the spectral representation method and an iterative algorithm to accurately and stably generate rough surfaces characterized by extensive skewness, kurtosis and autocorrelation lengths. The skewness and kurtosis range of the generated rough surface includes skewness and kurtosis of most engineering surfaces, such as worn surfaces and various machined surface and irregular engineering surfaces. A rough surface is easily generated <= 10 s.

关键词： Rough surface Skewness and kurtosis Autocorrelation function Analytical function Spectral representation method (SRM) iterative algorithm

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One step inversion free iterative algorithm for computing generalised bisymmetric solution for nonlinear matrix equations

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INTERNATIONAL JOURNAL OF CONTROL 2025年第4期98卷 915-924页

作者： Bayoumi, Ahmed M. E. Ramadan, Mohamed A. Ain Shams Univ Fac Educ Dept Math Cairo Egypt Menoufia Univ Fac Sci Dept Math & Comp Sci Shibin Al Kawm Egypt

In this paper, we investigate one step inversion free iterative algorithm for computing generalised bisymmetric solution to the nonlinear matrix equations (NLME) $ X + {AT}{X{ - q}}A + {BT}{X{ - q}}B = H ({q \ge 2} ) ... 详细信息

In this paper, we investigate one step inversion free iterative algorithm for computing generalised bisymmetric solution to the nonlinear matrix equations (NLME) $ X + {A<^>T}{X<^>{ - q}}A + {B<^>T}{X<^>{ - q}}B = H ({q \ge 2} ) $ X+ATX-qA+BTX-qB=H(q >= 2), where $ A,B,H $ A,B,H are given matrices, while $ X $ X is a generalised bisymmetric matrix to be computed. The necessary conditions for the existence of a generalised bisymmetric solution and the convergence of the suggested iterative method are derived. Some lemmas and theorems are provided and proved where the iterative solutions are obtained. Four numerical examples are presented to exhibit the effectiveness of the suggested method and to verify the theoretical findings of this paper.

关键词： Inversion free generalised bisymmetric solution iterative algorithm Newton's method Frobenius norm nonlinear matrix equation

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A SIMPLE iterative algorithm FOR MAXCUT

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Journal of Computational Mathematics 2024年第5期42卷 1277-1304页

作者： Sihong Shao Dong Zhang Weixi Zhang CAPT LMAM and School of Mathematical SciencesPeking UniversityBeijing 100871China LMAM and School of Mathematical Sciences Peking UniversityBeijing 100871China

We propose a simple iterative(SI)algorithm for the maxcut problem through fully using an equivalent continuous *** does not need rounding at all and has advantages that all subproblems have explicit analytic solutions,the cut values are monotonically updated and the iteration points converge to a local optima in finite steps via an appropriate subgradient *** experiments on G-set demonstrate the *** particular,the ratios between the best cut values achieved by SI and those by some advanced combinatorial algorithms in[***.,248(2017),365-403]are at least 0.986 and can be further improved to at least 0.997 by a preliminary attempt to break out of local optima.

关键词： Maxcut iterative algorithm Exact solution Subgradient selection Fractional programming

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iterative algorithm for fixed point problems of generalized nearly asymptotically nonexpansive mappings and solutions of a system of generalized nonlinear variational-like inclusions

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2022年第1期2022卷 1-42页

作者： Balooee, Javad Chang, Shih-sen Wang, Lin Univ Tehran Coll Sci Sch Math Stat & Comp Sci Tehran Iran China Med Univ Ctr Gen Educ Taichung 40402 Taiwan Yunnan Univ Finance & Econ Kunming 650321 Yunnan Peoples R China

This paper is devoted to the study of a class of generalized nonexpansive mappings called generalized nearly asymptotically nonexpansive mappings and to show that it properly includes the class of nearly asymptotically nonexpansive mappings. We investigate the problem of approximating a common element of the set of solutions of a system of generalized nonlinear variational-like inclusions involving P-eta-accretive mappings and of the set of fixed points of a generalized nearly asymptotically nonexpansive mapping. To this end, we suggest a new iterative algorithm with mixed errors. As an application of the obtained equivalence, we prove the strong convergence and stability of the sequence generated by the proposed iterative algorithm to a common point of the two sets mentioned above.

关键词： Generalized nearly asymptotically nonexpansive mapping Fixed point problem System of generalized nonlinear variational-like inclusions P-eta-accretive mapping iterative algorithm Graph convergence Resolvent operator technique Convergence analysis

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Total Least Squares algorithm for Errors-in-Variables Systems: iterative algorithm or Two-Step algorithm

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 10753-10763页

作者： Chen, Jing Na, Jing Li, Junhong Zhu, Quanmin Jiangnan Univ Sch Sci Wuxi 214122 Peoples R China Kunming Univ Sci & Technol Fac Mech & Elect Engn Kunming 650550 Peoples R China Nantong Univ Sch Elect Engn Nantong 226019 Peoples R China Univ West England Sch Engn Bristol BS16 1QY England

The total least squares (TLS) algorithm is a superior identification tool for low-order errors-in-variables (EIV) systems, where the estimate can be obtained by solving an eigenvector of the minimum eigenvalue of an augmented matrix. However, the TLS algorithm demonstrates inefficiency when applied to high-order EIV systems. This study introduces two innovative TLS algorithms: an iterative TLS algorithm, offering superior performance for low-order EIV models, and a two-step TLS algorithm, designed to effectively handle high-order EIV models. In comparison to the conventional TLS algorithm, these proposed methodologies present noteworthy advantages, including: 1) reduced computational costs, 2) the utilization of an iterative technique to calculate the inverse, and 3) the diversification of EIV identification methods. Simulation bench test examples are selected to show the efficacy of the proposed algorithms and transparent procedure for applications.

关键词： Eigenvalues and eigenfunctions Mathematical models Noise Computational modeling Convergence iterative algorithms Large-scale systems Cost function Automation Accuracy Errors-in-variables system total least squares iterative algorithm two-step algorithm eigenvalue calculation

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A new inversion-free iterative algorithm for the discrete algebraic Riccati equation

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IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION 2024年第1期41卷 149-164页

作者： Wang, Li Zhu, Yuli Hunan Univ Sci & Technol Sch Math & Computat Sci Hunan 411201 Peoples R China

In this paper, by the transformation form of the discrete algebraic Riccati equation (DARE), we propose a new inverse-free iterative algorithm to obtain the positive definite solution of the DARE. Furthermore, the monotone convergence is proved and convergence rate analysis is presented for the derived algorithm. Compared with some existing algorithms, numerical examples demonstrate the feasibility and effectiveness of our algorithm.

关键词： inverse-free discrete algebraic Riccati equation iterative algorithm convergence analysis

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Novel nonlinear wind power prediction based on improved iterative algorithm

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SYSTEMS SCIENCE & CONTROL ENGINEERING 2025年第1期13卷

作者： Fu, Zhen-yu Lin, Gui-quan Tian, Wei-da Pan, Zhi-hao Zhang, Wei-cong Guangdong Power Grid Co Ltd Zhanjiang Power Supply Bur Zhanjiang Peoples R China Huaiyin Inst Technol Fac Automat Huaian Peoples R China

To effectively improve the accuracy of wind power prediction and reduce the load on the power grid, a new nonlinear wind power prediction model based on an improved iterative learning algorithm was investigated. Firstly, the actual wind conditions are equated to a non-linear model. Using the concept of nonlinear decomposition, the nonlinear model is divided into many linear subdomain models while taking into account the nonlinear impacts of temperature, wind direction, altitude, and speed on the model. Next, using CRITIC weight analysis, the ideal weights are determined. Then, the linear sub-domain model is fitted into the full non-linear wind power prediction model equation by utilizing the least squares method. And the objective function of the iterative algorithm for iterative optimization search is derived from the prediction equations that were previously developed. The final enhanced iterative technique for nonlinear wind power prediction is produced by merging the iterative algorithm with the nonlinear decomposition. Finally, a comparative study of wind power prediction under different prediction models was carried out. The research results showed that the average absolute error of wind power prediction and the root mean square error were 4.5841% and 0.2301%, respectively. In particular, the prediction accuracy improved by 8.28%.

关键词： iterative algorithm wind power forecasting weighting analysis linear subdomain model nonlinear predictive model

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An Improved iterative algorithm for Identifying Strong H-Tensors

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COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION 2025年第4期7卷 1598-1614页

作者： Gong, Wenbin Li, Yan Wang, Yaqiang Baoji Univ Arts & Sci Sch Math & Informat Sci Baoji 721013 Shaanxi Peoples R China

Strong H-tensors play a significant role in identifying the positive definiteness of an even-order real symmetric tensor. In this paper, first, an improved iterative algorithm is proposed to determine whether a given tensor is a strong H-tensor, and the validity of the iterative algorithm is proved theoretically. Second, the iterative algorithm is employed to identify the positive definiteness of an even-order real symmetric tensor. Finally, numerical examples are presented to illustrate the advantages of the proposed algorithm.

关键词： Strong H-tensors iterative algorithm Positive diagonal matrix Symmetric tensors

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Explicit iterative algorithm with optimal tuning parameter for stochastic Lyapunov matrix equation

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NUMERICAL algorithmS 2025年 1-24页

作者： Chen, Zebin Sun, Hui-Jie Zhang, Jinxiu Chen, Xuesong Sun Yat Sen Univ Sch Aeronaut & Astronaut Guangzhou 510006 Peoples R China Guangdong Univ Technol Sch Math & Stat Guangzhou 510006 Peoples R China

In this study, a new explicit iterative algorithm with a tuning parameter is constructed to solve the Lyapunov matrix equation associated with the discrete-time stochastic systems. Firstly, the boundedness and monotonicity of the proposed algorithm under zero initial condition are studied when the corresponding stochastic system is asymptotical mean-square stable. In addition, some necessary and sufficient conditions are investigated for the convergence of the proposed algorithm. Furthermore, the optimal tuning parameter is studied to achieve the fastest convergence rate of the algorithm for some special cases, and for the general cases, two searching approaches are given to find the optimal tuning parameter. Finally, three numerical examples are taken to illustrate the correctness of the conclusions in this paper.

关键词： iterative algorithm Tuning parameter Sylvester matrix equations Lyapunov matrix equations Stochastic systems

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