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 -

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.