An iterative algorithm for generalized Hamiltonian solution of a class of generalized coupled Sylvester-conjugate matrix equations

In this work, we present an iterative algorithm to solve a class of generalized coupled Sylvester-conjugate matrix equations over the generalized Hamiltonian matrices. We show that if the equations are consistent, a generalized Hamiltonian solution can be obtained within finite iteration steps in the absence of round-offerrors for any initial generalized Hamiltonian matrix by the proposed iterative algorithm. Furthermore, we can obtain the minimum-norm generalized Hamiltonian solution by choosing the special initial matrices. Finally, numerical examples show that the iterative algorithm is effective. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This work presents an iterative algorithm for solving a class of generalized coupled Sylvester-conjugate matrix equations over generalized Hamiltonian matrices. It is shown that a generalized Hamiltonian solution can be obtained within finite iteration steps in the absence of round-off errors if the equations are consistent. By choosing special initial matrices, the minimum-norm solution can be obtained, and numerical examples demonstrate the effectiveness of the iterative algorithm.