TY - JOUR
T1 - Parameterized GSOR Method for a Class of Complex Symmetric Systems of Linear Equations
AU - Wu , Yujiang
AU - Zhang , Wei-Hong
AU - Li , Xi-An
AU - Yang , Ai-Li
JO - Journal of Mathematical Study
VL - 1
SP - 18
EP - 29
PY - 2019
DA - 2019/03
SN - 52
DO - http://doi.org/10.4208/jms.v52n1.19.02
UR - https://global-sci.org/intro/article_detail/jms/13045.html
KW - Complex linear systems, symmetric positive definite, spectral radius, convergence, preconditioning.
AB - <p style="text-align: justify;">A parameterized generalized successive overrelaxation (PGSOR) method
for a class of block two-by-two linear system is established in this paper. The convergence theorem of the method is proved under suitable assumptions on iteration
parameters. Besides, we obtain a functional equation between the parameters and
the eigenvalues of the iteration matrix for this method. Furthermore, an accelerated
variant of the PGSOR (APGSOR) method is also presented in order to raise the convergence rate. Finally, numerical experiments are carried out to confirm the theoretical
analysis as well as the feasibility and the efficiency of the PGSOR method and its variant.</p>