Hamideh Nasabzadeh - Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P. O. Box ۹۴۵۳۱۵۵۱۱۱, 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. ۴۴ (۲۰۱۵) ۲۶-۲۹] 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. ۲۴۸ (۲۰۱۴) ۶۰۲-۶۰۹], 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.

Non-Hermitian, HSS method, convergence Analysis, iterative Method