An iterative algorithm for generalized periodic multiple coupled Sylvester matrix equations

The paper is indicated to constructing a modified conjugate gradient iterative (MCG) algorithm to solve the generalized periodic multiple coupled Sylvester matrix equations. It can be proved that the proposed approach can find the solution within finite iteration steps in the absence of round-off errors. Furthermore, we provide a method for choosing the initial matrices to obtain the least Frobenius norm solution of the system. Some numerical examples are illustrated to show the performance of the proposed approach and its superiority over the existing method CG. (C) 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper presents a modified conjugate gradient iterative (MCG) algorithm for solving generalized periodic multiple coupled Sylvester matrix equations, which can find the solution within finite iteration steps without round-off errors and provides a method for choosing initial matrices. Numerical examples illustrate the superior performance of the proposed method.