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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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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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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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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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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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Fixed-point iterative algorithm for SVI model

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FINANCE RESEARCH LETTERS 2025年 80卷

作者： Yang, Shuzhen Zhang, Wenqing Shandong Univ Zhong Tai Secur Inst Financial Studies Jinan Peoples R China Shandong Univ Sch Math Jinan Peoples R China

The stochastic volatility inspired (SVI) model is widely used to fit the implied variance smile. Currently, most optimization algorithms for SVI models are strongly dependent on the input starting point. In this study, we develop an efficient iterative algorithm for the SVI model based on a fixed-point least-squares optimizer, further presenting the convergence results for this novel iterative algorithm under certain condition. The experimental evaluation results of our approach using market data demonstrate the advantages of the proposed fixed-point iterative algorithm over the Quasi-explicit SVI method.

关键词： iterative algorithm Stochastic volatility FPI-SVI algorithm Quasi-explicit SVI

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iterative algorithm for direction of arrival estimation with wideband chirp signals

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IEE PROCEEDINGS-RADAR SONAR AND NAVIGATION 2000年第5期147卷 233-238页

作者： Wang, G Xia, XG Univ Delaware Dept Elect & Comp Engn Newark DE 19716 USA

A time-frequency MUSIC algorithm with narrowband models for the estimation of direction of arrival (DOA) when the source signals are chirps has been developed by Amin et al. (1998, 1999). The present authors consider wideband models. The joint time-frequency analysis is first used to estimate the chirp rates of the source signals, and then the DOA is estimated by the MUSIC algorithm with an interative approach.

关键词： iterative methods chirp rates wideband chirp signals Interpolation and function approximation (numerical analysis) direction-of-arrival estimation array signal processing joint time-frequency analysis iterative algorithm time-frequency analysis DOA time-frequency MUSIC algorithm source signals Signal processing theory Signal processing and detection direction of arrival estimation

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iterative algorithm of solutions for a system of generalized mixed implicity equilibrium problems in reflexive Banach spaces

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APPLIED MATHEMATICS AND COMPUTATION 2012年第9期218卷 4953-4961页

作者： Ding, Xie Ping Sichuan Normal Univ Coll Math & Software Sci Chengdu 610066 Sichuan Peoples R China

In this paper, a new system of generalized mixed implicity equilibrium problems involving non-monotone set-valued mappings is introduced and studied in real reflexive Banach spaces. Following the idea of Moudafi, we consider a system of generalized equations problems and show its equivalence with the system of generalized mixed implicity equilibrium problems. By using a fixed point formulation of the system of generalized equation problems, a new iterative algorithm for solving the system of generalized mixed implicity equilibrium problems is suggested and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new and unify and generalize some recent results in this field. (C) 2011 Elsevier Inc. All rights reserved.

关键词： System of generalized mixed implicity equilibrium problems System of generalized equation problems iterative algorithm Reflexive Banach spaces

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iterative algorithm for finding approximate solutions of mixed quasi-variational-like inclusions

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2008年第4期56卷 942-952页

作者： Ceng, Lu-Chuan Guu, Sy-Ming Yao, Jen-Chih Yuan Ze Univ Coll Management Dept Business Adm Chungli 330 Taoyuan Hsien Taiwan Shanghai Normal Univ Dept Math Shanghai 200234 Peoples R China Natl Sun Yat Sen Univ Dept Appl Math Kaohsiung 804 Taiwan

In the present paper, we introduce the concept of eta-relaxed strong convexity of a differentiable functional and extend Ding and Yao's auxiliary variational inequality technique [X.P. Ding, J.C. Yao, Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces, Computers and Mathematics with Applications, 49 (2005), 857-869] to develop iterative algorithms for finding the approximate solutions to the mixed quasi-variational-like inclusion problem (in short, MQVLIP) in a Banach space. On the one hand, we establish a result on the existence of a solution to the equilibrium problem by virtue of well-known Brouwer's fixed-point theorem. Moreover, by using this result we derive the existence and uniqueness of a solution to the MQVLIP and the existence of the approximate solutions generated by the algorithm for the MQVLIP. On the other hand, we use the concepts of eta-relaxed strong convexity of a differentiable functional and eta-cocoercivity of a composite map to prove the strong convergence of the approximate solutions to the unique solution of the MQVLIP. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： mixed quasi-variational-like inclusion Brouwer's fixed-point theorem auxiliary variational inequality iterative algorithm Banach space

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iterative algorithm for generalized quasi-variational-like inclusions with fuzzy mappings in Banach spaces

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2006年第1期188卷 1-11页

作者： Kazmi, KR Aligarh Muslim Univ Dept Math Aligarh 202002 Uttar Pradesh India

In this paper, we introduce and study a class of generalized quasi-variational-like inclusions with fuzzy mappings in real Banach spaces and show its equivalence with a class of relations. Using this equivalence, we suggest and analyze an iterative algorithm for finding the approximate solution of this class of inclusions. Further, we prove the existence of solution of this class of inclusions and discuss the convergence criteria of iterative sequences generated by the iterative algorithm. (c) 2005 Elsevier B.V All rights reserved.

关键词： generalized quasi-variational-like inclusion fuzzy mappings iterative algorithm strongly eta-accretive mapping m-q-accretive mapping eta-proximal point mapping

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