Abstract
PurposeThis article proposes a relaxed gradient iterative (RGI) algorithm to solve coupled Sylvester-conjugate transpose matrix equations (CSCTME) with two unknowns.Design/methodology/approachThis article proposes a RGI algorithm to solve CSCTME with two unknowns.FindingsThe 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/implicationsThe introduced (RGI) algorithm is more efficient than the GI algorithm presented in Bayoumi (2014), where the author's method exhibits quick convergence behavior.Practical implicationsIn systems and control, Lyapunov matrix equations, Sylvester matrix equations and other matrix equations are commonly encountered.Social implicationsIn systems and control, Lyapunov matrix equations, Sylvester matrix equations and other matrix equations are commonly encountered.Originality/valueThis 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.
Subject
Computational Theory and Mathematics,Computer Science Applications,General Engineering,Software
Reference19 articles.
1. A theoretical and numerical study of complex and coupled forms of sylvester matrix equations using iterative algorithms,2014
2. Two relaxed gradient-based algorithms for the Hermitian and skew-Hermitian solutions of the linear matrix equation AXB+CXD=F;Iranian Journal of Science and Technology, Transactions A: Science,2019
3. Jacobi-gradient iterative algorithm for solving extended Sylvester-conjugate matrix equations;Applied Mathematics and Information Sciences,2021
4. An accelerated gradient-based iterative algorithm for solving extended Sylvester-conjugate matrix equations;Transactions of the Institute of Measurement and Control,2018
5. Gradient based iterative algorithms for solving a class of matrix equations;IEEE Transactions on Automatic Control,2005