TY - JOUR
T1 - A Class of Preconditioned TGHSS-Based Iteration Methods for Weakly Nonlinear Systems
AU - Min-Li Zeng & Guo-Feng Zhang
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 367
EP - 383
PY - 2018
DA - 2018/02
SN - 6
DO - http://doi.org/10.4208/eajam.150116.240516a
UR - https://global-sci.org/intro/article_detail/eajam/10805.html
KW - System of weakly nonlinear equations, GHSS iteration method, local convergence, inner iteration, outer iteration.
AB - <p style="text-align: justify;">In this paper, we first construct a preconditioned two-parameter generalized
Hermitian and skew-Hermitian splitting (PTGHSS) iteration method based on the
two-parameter generalized Hermitian and skew-Hermitian splitting (TGHSS) iteration
method for non-Hermitian positive definite linear systems. Then a class of PTGHSS-based
iteration methods are proposed for solving weakly nonlinear systems based on
separable property of the linear and nonlinear terms. The conditions for guaranteeing
the local convergence are studied and the quasi-optimal iterative parameters are derived. Numerical experiments are implemented to show that the new methods are feasible and effective for large scale systems of weakly nonlinear systems.</p>