4.7 Article

On the relaxed gradient-based iterative methods for the generalized coupled Sylvester-transpose matrix equations

Related references

Note: Only part of the references are listed.
Article Engineering, Electrical & Electronic

Optimal Adaptive Filtering Algorithm by Using the Fractional-Order Derivative

Xiao Zhang et al.

Summary: This study builds on previous work in filter design and proposes a solution to the problem of correlated noise disturbance by introducing a linear prefilter to obtain unbiased estimate of the filter weight. Moreover, compared to integer-order-based adaptive algorithms, the fractional-order-based algorithms show better performance.

IEEE SIGNAL PROCESSING LETTERS (2022)

Article Mathematics, Interdisciplinary Applications

Complex Dynamics of a Four-Dimensional Circuit System

Haijun Wang et al.

Summary: By combining qualitative analysis and numerical techniques, this study revisits a four-dimensional circuit system proposed by Ma et al. (2016) and uncovers previously uninvestigated rich dynamics such as pitchfork bifurcation, Hopf bifurcation, and singularly degenerate heteroclinic cycles. The main contributions include the discovery of globally exponentially attractive set, heteroclinic orbits, and potential hidden attractors, as well as insights into the forming mechanism of hyperchaos.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2021)

Article Mathematics, Applied

Iterative solution to a class of complex matrix equations and its application in time-varying linear system

Wenli Wang et al.

Summary: A relaxed gradient based iterative algorithm is proposed to solve a complex matrix equation, and the necessary conditions for convergence are determined. Numerical results confirm the efficiency of the new method in addressing the problem.

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING (2021)

Article Mathematics, Applied

Convergence analysis of a gradient iterative algorithm with optimal convergence factor for a generalized Sylvester-transpose matrix equation

Nunthakarn Boonruangkan et al.

Summary: In this study, an iterative algorithm based on gradients and hierarchical identification principle is proposed to solve a generalized Sylvester-transpose matrix equation with rectangular coefficient matrices. The convergence analysis reveals that the algorithm converges to a unique solution if the convergence factor is chosen appropriately. The algorithm's performance is theoretically analyzed in terms of convergence rate and error estimations, with the optimal convergence factor chosen to achieve the fastest asymptotic behavior. Numerical experiments demonstrate the capability and efficiency of the proposed algorithm compared to recent gradient-based iterative algorithms.

AIMS MATHEMATICS (2021)

Article Computer Science, Artificial Intelligence

On the investigation of activation functions in gradient neural network for online solving linear matrix equation

Zhiguo Tan et al.

NEUROCOMPUTING (2020)

Article Computer Science, Software Engineering

Survey on geometric iterative methods and their applications

Hongwei Lin et al.

COMPUTER-AIDED DESIGN (2018)

Article Automation & Control Systems

The relaxed gradient-based iterative algorithms for a class of generalized coupled Sylvester-conjugate matrix equations

Baohua Huang et al.

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS (2018)

Article Engineering, Multidisciplinary

Developing BiCOR and CORS methods for coupled Sylvester-transpose and periodic Sylvester matrix equations

Masoud Hajarian

APPLIED MATHEMATICAL MODELLING (2015)

Article Mathematics, Applied

Reduced-rank gradient-based algorithms for generalized coupled Sylvester matrix equations and its applications

Huamin Zhang

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2015)

Article Automation & Control Systems

Matrix GPBiCG algorithms for solving the general coupled matrix equations

Masoud Hajarian

IET CONTROL THEORY AND APPLICATIONS (2015)

Article Mathematics, Applied

Matrix form of the CGS method for solving general coupled matrix equations

Masoud Hajarian

APPLIED MATHEMATICS LETTERS (2014)

Article Automation & Control Systems

A RELAXED GRADIENT BASED ALGORITHM FOR SOLVING EXTENDED SYLVESTER-CONJUGATE MATRIX EQUATIONS

Mohamed A. Ramadan et al.

ASIAN JOURNAL OF CONTROL (2014)

Article Automation & Control Systems

Gradient-based iterative algorithm for a class of the coupled matrix equations related to control systems

Feng Ding et al.

IET CONTROL THEORY AND APPLICATIONS (2014)

Article Mathematics, Applied

Finite iterative method for solving coupled Sylvester-transpose matrix equations

Caiqin Song et al.

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING (2014)

Article Engineering, Multidisciplinary

Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling

Feng Ding

APPLIED MATHEMATICAL MODELLING (2013)

Article Mathematics, Applied

The generalized QMRCGSTAB algorithm for solving Sylvester-transpose matrix equations

Masoud Hajarian

APPLIED MATHEMATICS LETTERS (2013)

Article Mathematics, Applied

The coupled Sylvester-transpose matrix equations over generalized centro-symmetric matrices

Fatemeh Panjeh Ali Beik et al.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS (2013)

Article Automation & Control Systems

Matrix iterative methods for solving the Sylvester-transpose and periodic Sylvester matrix equations

Masoud Hajarian

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS (2013)

Article Automation & Control Systems

A RELAXED GRADIENT BASED ALGORITHM FOR SOLVING SYLVESTER EQUATIONS

Qiang Niu et al.

ASIAN JOURNAL OF CONTROL (2011)

Article Mathematics, Applied

Gradient-based maximal convergence rate iterative method for solving linear matrix equations

Bin Zhou et al.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS (2010)

Article Mathematics, Applied

Gradient based iterative solutions for general linear matrix equations

Li Xie et al.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2009)

Article Automation & Control Systems

Gradient based iterative algorithm for solving coupled matrix equations

Bin Zhou et al.

SYSTEMS & CONTROL LETTERS (2009)

Article Mathematics, Applied

Convergence of gradient-based iterative solution of coupled Markovian jump Lyapunov equations

Bin Zhou et al.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2008)

Article Mathematics, Applied

Sylvester Tikhonov-regularization methods in image restoration

A. Bouhamidi et al.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2007)

Article Mathematics, Applied

Iterative orthogonal direction methods for Hermitian minimum norm solutions of two consistent matrix equations

Yuan-Bel Deng et al.

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS (2006)

Article Automation & Control Systems

On iterative solutions of general coupled matrix equations

F Ding et al.

SIAM JOURNAL ON CONTROL AND OPTIMIZATION (2006)

Article Automation & Control Systems

Gradient based iterative algorithms for solving a class of matrix equations

F Ding et al.

IEEE TRANSACTIONS ON AUTOMATIC CONTROL (2005)

Article Mathematics, Applied

The solution to the matrix equation AV+BW = EV J+R

GR Duan

APPLIED MATHEMATICS LETTERS (2004)