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Volume 52, Issue 1
Parameterized GSOR Method for a Class of Complex Symmetric Systems of Linear Equations

Yujiang Wu, Wei-Hong Zhang, Xi-An Li & Ai-Li Yang

DOI: 10.4208/jms.v52n1.19.02

J. Math. Study, 52 (2019), pp. 18-29.

Published online: 2019-03

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  • Abstract

A parameterized generalized successive overrelaxation (PGSOR) method for a class of block two-by-two linear system is established in this paper. The convergence theorem of the method is proved under suitable assumptions on iteration parameters. Besides, we obtain a functional equation between the parameters and the eigenvalues of the iteration matrix for this method. Furthermore, an accelerated variant of the PGSOR (APGSOR) method is also presented in order to raise the convergence rate. Finally, numerical experiments are carried out to confirm the theoretical analysis as well as the feasibility and the efficiency of the PGSOR method and its variant.

  • Keywords

Complex linear systems, symmetric positive definite, spectral radius, convergence, preconditioning.

  • AMS Subject Headings

65F10, 65F50, 65F08

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

myjaw@lzu.edu.cn (Yujiang Wu)

zhangwh13@lzu.edu.cn (Wei-Hong Zhang)

lixian9131@163.com (Xi-An Li)

yangaili@lzu.edu.cn (Ai-Li Yang)

  • BibTex
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  • TXT
@Article{JMS-52-18, author = {Wu , YujiangZhang , Wei-HongLi , Xi-An and Yang , Ai-Li}, title = {Parameterized GSOR Method for a Class of Complex Symmetric Systems of Linear Equations}, journal = {Journal of Mathematical Study}, year = {2019}, volume = {52}, number = {1}, pages = {18--29}, abstract = {

A parameterized generalized successive overrelaxation (PGSOR) method for a class of block two-by-two linear system is established in this paper. The convergence theorem of the method is proved under suitable assumptions on iteration parameters. Besides, we obtain a functional equation between the parameters and the eigenvalues of the iteration matrix for this method. Furthermore, an accelerated variant of the PGSOR (APGSOR) method is also presented in order to raise the convergence rate. Finally, numerical experiments are carried out to confirm the theoretical analysis as well as the feasibility and the efficiency of the PGSOR method and its variant.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v52n1.19.02}, url = {http://global-sci.org/intro/article_detail/jms/13045.html} }
TY - JOUR T1 - Parameterized GSOR Method for a Class of Complex Symmetric Systems of Linear Equations AU - Wu , Yujiang AU - Zhang , Wei-Hong AU - Li , Xi-An AU - Yang , Ai-Li JO - Journal of Mathematical Study VL - 1 SP - 18 EP - 29 PY - 2019 DA - 2019/03 SN - 52 DO - http://doi.org/10.4208/jms.v52n1.19.02 UR - https://global-sci.org/intro/article_detail/jms/13045.html KW - Complex linear systems, symmetric positive definite, spectral radius, convergence, preconditioning. AB -

A parameterized generalized successive overrelaxation (PGSOR) method for a class of block two-by-two linear system is established in this paper. The convergence theorem of the method is proved under suitable assumptions on iteration parameters. Besides, we obtain a functional equation between the parameters and the eigenvalues of the iteration matrix for this method. Furthermore, an accelerated variant of the PGSOR (APGSOR) method is also presented in order to raise the convergence rate. Finally, numerical experiments are carried out to confirm the theoretical analysis as well as the feasibility and the efficiency of the PGSOR method and its variant.

Wu , YujiangZhang , Wei-HongLi , Xi-An and Yang , Ai-Li. (2019). Parameterized GSOR Method for a Class of Complex Symmetric Systems of Linear Equations. Journal of Mathematical Study. 52 (1). 18-29. doi:10.4208/jms.v52n1.19.02
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