An iterative algorithm for generalized periodic multiple coupled Sylvester matrix equations. Issue 10 (July 2021)

• Record Type: Journal Article
• Authors: Chen, Xuesong; Chen, Zebin
• Is Part Of: Journal of the Franklin Institute. Volume 358:Issue 10(2021)
• Page Start: 5513
• Page End: 5531
• Publication Date: 2021-07
• Subjects: Sylvester matrix equation -- Conjugate gradient -- Iterative algorithm -- Least Frobenius norm solution; Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2021.05.012
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: 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.