TY - JOUR
T1 - Shift-Splitting Iteration Method and Its Variants for Solving Continuous Sylvester Equations
AU - Li , Xu
AU - He , Ning
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 367
EP - 380
PY - 2022
DA - 2022/02
SN - 12
DO - http://doi.org/10.4208/eajam.050821.070122
UR - https://global-sci.org/intro/article_detail/eajam/20259.html
KW - Continuous Sylvester equation, shift-splitting iteration, inexact iteration, convergence.
AB - <p style="text-align: justify;">A shift-splitting iteration method for solving large sparse continuous Sylvester
equations is developed. This single-step iteration algorithm demonstrates a better computational efficiency than the previously used two-step iterative methods. We also propose two variants — viz. inexact and accelerated shift-splitting iteration methods. The
convergence properties of all algorithms are studied and the quasi-optimal iteration parameter of shift-splitting is derived. Numerical examples demonstrate the efficiencies of
the three methods, especially for equations with ill-conditioned coefficient matrices.</p>