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This article proposes a relaxed gradient iterative (RGI) algorithm to solve coupled Sylvester-conjugate transpose matrix equations (CSCTME) with two unknowns.
Abstract
Purpose
This article proposes a relaxed gradient iterative (RGI) algorithm to solve coupled Sylvester-conjugate transpose matrix equations (CSCTME) with two unknowns.
Design/methodology/approach
This article proposes a RGI algorithm to solve CSCTME with two unknowns.
Findings
The introduced (RGI) algorithm is more efficient than the gradient iterative (GI) algorithm presented in Bayoumi (2014), where the author's method exhibits quick convergence behavior.
Research limitations/implications
The introduced (RGI) algorithm is more efficient than the GI algorithm presented in Bayoumi (2014), where the author's method exhibits quick convergence behavior.
Practical implications
In systems and control, Lyapunov matrix equations, Sylvester matrix equations and other matrix equations are commonly encountered.
Social implications
In systems and control, Lyapunov matrix equations, Sylvester matrix equations and other matrix equations are commonly encountered.
Originality/value
This article proposes a relaxed gradient iterative (RGI) algorithm to solve coupled Sylvester conjugate transpose matrix equations (CSCTME) with two unknowns. For any initial matrices, a sufficient condition is derived to determine whether the proposed algorithm converges to the exact solution. To demonstrate the effectiveness of the suggested method and to compare it with the gradient-based iterative algorithm proposed in [6] numerical examples are provided.
Details
Keywords
The purpose of this paper is to obtain an iterative algorithm to find the solution of the coupled Sylvester-like matrix equations.
Abstract
Purpose
The purpose of this paper is to obtain an iterative algorithm to find the solution of the coupled Sylvester-like matrix equations.
Design/methodology/approach
In this work, the matrix form of the conjugate direction (CD) algorithm to find the solution X of the coupled Sylvester-like matrix equations:
Findings
It is proven that the algorithm converges to the solution within a finite number of iterations in the absence of round-off errors. Finally, four numerical examples were used to test the proficiency and convergence of the established algorithm.
Originality/value
The numerical examples have led the author to believe that the generalized CD (GCD) algorithm is efficient and it converges more rapidly in comparison with the CGNR and CGNE algorithms.
Details