A new iteration method for solving non-Hermitian positive definite linear systems

Document Type : Research Article


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


In this paper, based on the single-step Hermitian and Skew-Hermitian (SHSS) iteration method [C.-X. Li, S.-L. Wu, A single-step method for non-Hermitian positive definite linear systems, Appl. Math. Lett. 44 (2015) 26-29] and by using the 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], a new method (GT-SHSS) is introduced to solve non-Hermitian positive definite linear systems. The convergence properties of the new method are discussed. We show that by using suitable parameters, the GT-SHSS iteration method is faster than the corresponding SHSS iteration method. The numerical examples confirm the effectiveness of the new method.