Article
Mathematics, Applied
Tongxin Yan, Changfeng Ma
Summary: This work presents an iterative algorithm for solving a class of generalized coupled Sylvester-conjugate matrix equations over generalized Hamiltonian matrices. It is shown that a generalized Hamiltonian solution can be obtained within finite iteration steps in the absence of round-off errors if the equations are consistent. By choosing special initial matrices, the minimum-norm solution can be obtained, and numerical examples demonstrate the effectiveness of the iterative algorithm.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Automation & Control Systems
Xuesong Chen, Zebin Chen
Summary: This paper presents a modified conjugate gradient iterative (MCG) algorithm for solving generalized periodic multiple coupled Sylvester matrix equations, which can find the solution within finite iteration steps without round-off errors and provides a method for choosing initial matrices. Numerical examples illustrate the superior performance of the proposed method.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Zebin Chen, Xuesong Chen
Summary: In this note, the authors point out the insufficient value range of the iterative factor delta in a previous study and rederive the proof process to obtain the correct range. By introducing a new scaling method, the value range of delta is significantly increased.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Computer Science, Interdisciplinary Applications
Ahmed M. E. Bayoumi
Summary: This article proposes a relaxed gradient iterative (RGI) algorithm to solve coupled Sylvester-conjugate transpose matrix equations (CSCTME) with two unknowns. The introduced algorithm is more efficient than the gradient iterative (GI) algorithm presented in Bayoumi (2014), where the author's method exhibits quick convergence behavior.
ENGINEERING COMPUTATIONS
(2023)
Article
Mathematics, Applied
Wenli Wang, Caiqin Song
Summary: This paper proposes a modified relaxed gradient based iterative (MRGI) algorithm for solving the coupled Sylvester-conjugate matrix equations (CSCMEs) based on the hierarchical identification principle. The convergence analysis shows that the proposed algorithm is effective for any initial matrices. Furthermore, the MRGI algorithm is applied to a more general case of CSCMEs and a sufficient condition is provided to guarantee the convergence of the iterative solution to the exact solution. Numerical experiments demonstrate that the MRGI algorithm outperforms three existing algorithms in terms of efficiency and accuracy, which were presented by Wu et al. (2010) and Huang and Ma (2018). Additionally, an application of the MRGI algorithm in discrete-time antilinear system is derived.
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
(2023)
Article
Multidisciplinary Sciences
Jing Jiang, Ning Li
Summary: In this paper, an iterative algorithm is proposed for solving the generalized (P, Q)-reflexive solution group of quaternion matrix equations. The algorithm can derive the generalized (P, Q)-reflexive solution group and the least Frobenius norm generalized (P, Q)-reflexive solution group by choosing appropriate initial matrices. Moreover, the optimal approximate generalized (P, Q)-reflexive solution group to a given matrix group can be obtained by computing the least Frobenius norm generalized (P, Q)-reflexive solution group of a reestablished system of matrix equations. Numerical examples are provided to illustrate the effectiveness of the algorithm.
Article
Automation & Control Systems
Ahmed M. E. Bayoumi, Mohamed Ramadan
Summary: In this research, we focus on finding solutions to coupled Sylvester complex matrix equations with conjugates of two unknowns. An iterative algorithm is used to obtain the solutions when the matrix equations are consistent. A condition is established to ensure the convergence of the proposed method. Numerical examples are provided to demonstrate the efficiency of the described iterative technique.
Article
Mathematics, Applied
Wenli Wang, Caiqin Song
Summary: This paper proposes the Jacobi gradient based iterative (JGI) algorithm and accelerated Jacobi gradient based iterative (AJGI) algorithm for solving the discrete-time periodic Sylvester matrix equations. The algorithms are shown to be convergent for any initial matrix under certain conditions, and their effectiveness and superiority are demonstrated through numerical examples.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics
Malik Zaka Ullah
Summary: This article investigates a new solver in the form of an iterative method for solving an important nonlinear matrix equation, discussing the minimal and maximal solutions as Hermitian positive definite matrices. The convergence of the scheme is confirmed, supported by several numerical tests.
Article
Mathematics, Applied
Xiaowen Wu, Zhengge Huang, Jingjing Cui, Yanping Long
Summary: This paper proposes the weighted, relaxed gradient-based iterative (WRGI) algorithm to solve the generalized coupled conjugate and transpose Sylvester matrix equations. It determines the necessary and sufficient conditions for the convergence of the WRGI algorithm and presents some sufficient convergence conditions. Moreover, it provides the optimal step size and convergence factor of the WRGI algorithm and demonstrates its effectiveness, feasibility and superiority through numerical examples.
Article
Multidisciplinary Sciences
Mahmoud Saad Mehany, Qing-Wen Wang
Summary: The current study investigates the solvability conditions and the general solution of three symmetrical systems of coupled Sylvester-like quaternion matrix equations. An algorithm and a numerical example are constructed over the quaternions to validate the results of this paper.
Article
Mathematics, Applied
Masoud Hajarian, Anthony Theodore Chronopoulos
Summary: The study focuses on the generalized conjugate directions method for solving coupled Sylvester matrix equations, showing that the method can compute least-squares partially bisymmetric solutions with a prescribed submatrix constraint and converge within a finite number of iterations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics
Tao Li, Qing-Wen Wang, Xin-Fang Zhang
Summary: This paper proposes a modified conjugate residual method for solving the generalized coupled Sylvester tensor equations, and further derives a preconditioned modified conjugate residual method based on Kronecker product approximations. Theoretical analysis and numerical results demonstrate that our methods outperform the traditional conjugate gradient method in terms of convergence rate and computational efficiency.
Article
Mathematics, Applied
Tao Li, Chi-Hua Feng, Xin-Fang Zhang
Summary: This paper discusses the generalized coupled Sylvester tensor equations and introduces two specific algorithms for solving them. It is shown that these methods converge to the exact solution group within finite steps when there are no round-off errors and the equations are consistent. Through numerical examples, the effectiveness of the proposed methods is demonstrated in color image restoration problems and randomly generated data.
Article
Mathematics
Marzieh Dehghani-Madiseh
Summary: In this paper, the interval coupled Sylvester matrix equations, including the (generalized) Sylvester and Lyapunov matrix equations in both real and interval forms, are investigated. A fast and efficient approach for enclosing the solution set of the interval coupled Sylvester matrix equations is presented, assuming certain matrices are simultaneously diagonalizable. The proposed approach, a modification of the Krawczyk operator, significantly reduces computational complexity. Numerical tests are provided to demonstrate the effectiveness of the approach.
LINEAR & MULTILINEAR ALGEBRA
(2023)
Article
Automation & Control Systems
Masoud Hajarian
ASIAN JOURNAL OF CONTROL
(2017)
Article
Mathematics
Masoud Hajarian
LINEAR & MULTILINEAR ALGEBRA
(2018)
Article
Automation & Control Systems
Masoud Hajarian
ASIAN JOURNAL OF CONTROL
(2020)
Article
Mathematics, Applied
Masoud Hajarian
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2019)
Article
Automation & Control Systems
Masoud Hajarian
TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL
(2020)
Article
Engineering, Multidisciplinary
Zeynab Dalvand, Masoud Hajarian
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
(2020)
Article
Mathematics, Applied
Zeynab Dalvand, Masoud Hajarian, Jose E. Roman
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2020)
Article
Mathematics, Applied
Masoud Hajarian, Anthony Theodore Chronopoulos
Summary: The study focuses on the generalized conjugate directions method for solving coupled Sylvester matrix equations, showing that the method can compute least-squares partially bisymmetric solutions with a prescribed submatrix constraint and converge within a finite number of iterations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Automation & Control Systems
Shahram Hosseini, M. Navabi, Masoud Hajarian
Summary: A novel online robust meta-heuristic adaptive Bi-CGSTAB algorithm is proposed in this paper for model parameter and attitude estimation simultaneously. This method uses information from previous iterations to set solving steps towards local optimum, leading to a broader and more intelligent search in the Krylov subspace. Numerical results show higher performance and accuracy compared to other methods discussed.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
(2022)
Article
Automation & Control Systems
Shahram Hosseini, M. Navabi, Masoud Hajarian
Summary: In this paper, a new online robust meta-heuristic adaptive LSQR (ORALSQR) estimation method is proposed for simultaneous estimation of a multi input/output linear dynamic model and system state variables. Numerical results show that this method outperforms the LS and RLS based estimation methods mentioned in this paper in terms of accuracy and robustness.
IET CONTROL THEORY AND APPLICATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Raziyeh Erfanifar, Masoud Hajarian
Summary: This paper studies a common nonlinear matrix equation and proposes two iterative schemes to solve it, while proving the convergence of these schemes.
ENGINEERING COMPUTATIONS
(2023)
Article
Automation & Control Systems
Raziyeh Erfanifar, Masoud Hajarian
Summary: This study presents schemes based on the Hermitian and skew-Hermitian splitting to solve the quadratic matrix equation (QME), which is important in various fields. The results show that the proposed schemes converge to the solutions of the QME, and their applicability is verified through examples.
IET CONTROL THEORY AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Raziyeh Erfanifar, Masoud Hajarian, Khosro Sayevand
Summary: In this work, a family of fourth-order methods is proposed to solve nonlinear equations, which satisfy the Kung-Traub optimality conjecture. The efficiency indices of the methods are increased by developing them into memory methods. The methods are then extended to multi-step methods for solving systems of problems. Numerical examples are provided to confirm the theoretical results, and the methods are applied to solve nonlinear problems related to the numerical approximation of fractional differential equations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Zeynab Dalvand, Masoud Hajarian
Summary: In this paper, we establish Newton-like and inexact Newton-like methods for solving a type of parameterized generalized inverse eigenvalue problem, and discuss their convergence properties. Through testing the performance and effectiveness of the algorithms on three numerical examples, it is found that the inexact Newton-like method can improve efficiency.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Automation & Control Systems
Masoud Hajarian
ASIAN JOURNAL OF CONTROL
(2018)
