Volume 10, Issue 3
Extrapolation Accelerated PRESB Method for Solving a Class of Block Two-by-Two Linear Systems

East Asian J. Appl. Math., 10 (2020), pp. 520-531.

Published online: 2020-06

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• Abstract

We use extrapolation acceleration technique to speed up the preconditioned square block matrix splitting iteration method for two-by-two block linear systems. It is shown that for relaxation parameter $ω$ = 4/3, the convergence factor of the iteration method under consideration is 1/3. This yields the robustness and efficiency of the method. Numerical examples confirm the theoretical results and demonstrate the effectiveness of the approach developed.

• Keywords

PRESB preconditioner, two-by-two block matrix, spectral radius, iteration method, convergence factor.

65F10, 65F50, 65W05

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@Article{EAJAM-10-520, author = {Liao , Li-Dan and Zhang , Guo-Feng and Wang , Xiang}, title = {Extrapolation Accelerated PRESB Method for Solving a Class of Block Two-by-Two Linear Systems}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {3}, pages = {520--531}, abstract = {

We use extrapolation acceleration technique to speed up the preconditioned square block matrix splitting iteration method for two-by-two block linear systems. It is shown that for relaxation parameter $ω$ = 4/3, the convergence factor of the iteration method under consideration is 1/3. This yields the robustness and efficiency of the method. Numerical examples confirm the theoretical results and demonstrate the effectiveness of the approach developed.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.280519.180120}, url = {http://global-sci.org/intro/article_detail/eajam/16980.html} }
TY - JOUR T1 - Extrapolation Accelerated PRESB Method for Solving a Class of Block Two-by-Two Linear Systems AU - Liao , Li-Dan AU - Zhang , Guo-Feng AU - Wang , Xiang JO - East Asian Journal on Applied Mathematics VL - 3 SP - 520 EP - 531 PY - 2020 DA - 2020/06 SN - 10 DO - http://doi.org/10.4208/eajam.280519.180120 UR - https://global-sci.org/intro/article_detail/eajam/16980.html KW - PRESB preconditioner, two-by-two block matrix, spectral radius, iteration method, convergence factor. AB -

We use extrapolation acceleration technique to speed up the preconditioned square block matrix splitting iteration method for two-by-two block linear systems. It is shown that for relaxation parameter $ω$ = 4/3, the convergence factor of the iteration method under consideration is 1/3. This yields the robustness and efficiency of the method. Numerical examples confirm the theoretical results and demonstrate the effectiveness of the approach developed.

Li-DanLiao, Guo-FengZhang & XiangWang. (2020). Extrapolation Accelerated PRESB Method for Solving a Class of Block Two-by-Two Linear Systems. East Asian Journal on Applied Mathematics. 10 (3). 520-531. doi:10.4208/eajam.280519.180120
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