TY - JOUR
T1 - Positive Definite and Semi-Definite Splitting Methods for Non-Hermitian Positive Definite Linear Systems
AU - Huang , Na
AU - Ma , Changfeng
JO - Journal of Computational Mathematics
VL - 3
SP - 300
EP - 316
PY - 2016
DA - 2016/06
SN - 34
DO - http://doi.org/10.4208/jcm.1511-m2015-0299
UR - https://global-sci.org/intro/article_detail/jcm/9797.html
KW - Linear systems, Splitting method, Non-Hermitian matrix, Positive definite
matrix, Positive semi-definite matrix, Convergence analysis.
AB - <p style="text-align: justify;">In this paper, we further generalize the technique for constructing the normal (or positive definite) and skew-Hermitian splitting iteration method for solving large sparse non-Hermitian positive definite system of linear equations. By introducing a new splitting, we establish a class of efficient iteration methods, called positive definite and semi-definite splitting (PPS) methods, and prove that the sequence produced by the PPS method converges unconditionally to the unique solution of the system. Moreover, we propose two kinds of typical practical choices of the PPS method and study the upper bound of the spectral radius of the iteration matrix. In addition, we show the optimal parameters such that the spectral radius achieves the minimum under certain conditions. Finally, some numerical examples are given to demonstrate the effectiveness of the considered methods.</p>