An accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations
Authors
Abstract:
In this paper, an accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations is proposed. The convergence analysis of the algorithm is investigated. We show that the proposed algorithm converges to the exact solution for any initial value under certain assumptions. Finally, some numerical examples are given to demonstrate the behavior of the proposed method and to support the theoretical results of this paper.
similar resources
Gradient Based Iterative Algorithm for Solving the Generalized Coupled Sylvester-transpose and Conjugate Matrix Equations over Reflexive (anti-reflexive) Matrices
Linear matrix equations play an important role in many areas, such as control theory, system theory, stability theory and some other fields of pure and applied mathematics. In the present paper, we consider the generalized coupled Sylvestertranspose and conjugate matrix equations Tν(X) = Fν , ν = 1, 2, . . . , N, where X = (X1, X2, . . . , Xp) is a group of unknown matrices and for ν = 1, 2, . ...
full textGradient based iterative algorithm for solving coupled matrix equations
This paper is concerned with iterative methods for solving a class of coupled matrix equations including the well-known coupled Markovian jump Lyapunov matrix equations as special cases. The proposed method is developed from an optimization point of view and contains the well-known Jacobi iteration, Gauss–Seidel iteration and some recently reported iterative algorithms by using the hierarchical...
full textAn Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations
An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations AXB − CYD,EXF − GYH M,N , which includes Sylvester and Lyapunov matrix equations as special cases, over generalized reflexive matrices X and Y . When the matrix equations are consistent, for any initial generalized reflexive matrix pair X1, Y1 , the generalized reflexive solutions can be obtained b...
full textThe coupled Sylvester-transpose matrix equations over generalized centro-symmetric matrices
In this paper, we present an iterative algorithm for solving the following coupled Sylvester-transpose matrix equations q ∑ j=1 ( AijXjBij + CijX j Dij ) = Fi, i = 1, 2, . . . , p, over the generalized centro-symmetric matrix group (X1, X2, . . . , Xq). The solvability of the problem can be determined by the proposed algorithm, automatically. If the coupled Sylvester-transpose matrix equations ...
full textIterative least-squares solutions of coupled Sylvester matrix equations
In this paper, we present a general family of iterative methods to solve linear equations, which includes the well-known Jacobi and Gauss–Seidel iterations as its special cases. The methods are extended to solve coupled Sylvester matrix equations. In our approach, we regard the unknown matrices to be solved as the system parameters to be identified, and propose a least-squares iterative algorit...
full textFinite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices
A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$. An $ntimes n$ complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$). In this paper, we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...
full textMy Resources
Journal title
volume 08 issue 02
pages 117- 126
publication date 2019-06-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023