on the gtsor-like method for the augmented systems

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 ecient than the sor-like method.