East Asian J. Appl. Math., 12 (2022), pp. 367-380.
Published online: 2022-02
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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.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.050821.070122}, url = {http://global-sci.org/intro/article_detail/eajam/20259.html} }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.