On the GTSOR-like Method for the Augmented systems

Document Type : Research Paper


Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P. O. Box 9453155111 Bojnord, Iran;



In this paper, by using SOR-Like method that introduced by Golub, Wu and Yuan and generalized Taylor expansion method for solving linear systems [F.Toutounian, H. Nasabzadeh, A new method based on the
generalized Taylor expansion for computing a series solution of linear systems,
Appl. Math. Comput. 248 (2014) 602-609], the GTSOR-Like method is proposed for augmented systems. The convergence analysis and the choice of the
parameters of the new method are discussed. While there is no guarantee the
SOR-Like method converges for the negative parameter, ω additional parameters of the new method can be adjusted for the corresponding GTSOR-Like
method to converge. Finally, numerical examples are given to show that the
new method is much more efficient than the SOR-Like method.