Relaxed gradient-based iterative solutions to coupled Sylvester-conjugate transpose matrix equations of 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.

Citation

Bayoumi, A.M.E. (2023), "Relaxed gradient-based iterative solutions to coupled Sylvester-conjugate transpose matrix equations of two unknowns", Engineering Computations, Vol. 40 No. 9/10, pp. 2776-2793. https://doi.org/10.1108/EC-07-2023-0370