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Volume 12, Issue 2
Shift-Splitting Iteration Method and Its Variants for Solving Continuous Sylvester Equations

Xu Li & Ning He

East Asian J. Appl. Math., 12 (2022), pp. 367-380.

Published online: 2022-02

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  • Abstract

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.

  • AMS Subject Headings

15A24, 15A30, 15A69, 65F10, 65F30, 65F50, 65H10

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-12-367, author = {Li , Xu and He , Ning}, title = {Shift-Splitting Iteration Method and Its Variants for Solving Continuous Sylvester Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {2}, pages = {367--380}, abstract = {

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} }
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.

Xu Li & Ning He. (2022). Shift-Splitting Iteration Method and Its Variants for Solving Continuous Sylvester Equations. East Asian Journal on Applied Mathematics. 12 (2). 367-380. doi:10.4208/eajam.050821.070122
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