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Volume 48, Issue 1
Self-Adaptive Extrapolated Gauss-Seidel Iterative Methods

Guo-Yan Meng & Rui-Ping Wen

DOI: 10.4208/jms.v48n1.15.02

J. Math. Study, 48 (2015), pp. 18-29.

Published online: 2015-03

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  • Abstract

In this paper, we consider a self-adaptive extrapolated Gauss-Seidel method for solving the Hermitian positive definite linear systems. Based on optimization models, self-adaptive optimal factor is given. Moreover, we prove the convergence of the self-adaptive extrapolated Gauss-Seidel method without any constraints on optimal factor. Finally, the numerical examples show that the self-adaptive extrapolated Gauss-Seidel method is effective and practical in iteration number.

  • Keywords

Hermitian positive definite, Gauss-Seidel iteration, self-adaptive, extrapolated, linear systems.

  • AMS Subject Headings

65F10, 65F50,15A06

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wenrp@tynu.edu.cn (Rui-Ping Wen)

  • BibTex
  • RIS
  • TXT
@Article{JMS-48-18, author = {Meng , Guo-Yan and Wen , Rui-Ping}, title = {Self-Adaptive Extrapolated Gauss-Seidel Iterative Methods}, journal = {Journal of Mathematical Study}, year = {2015}, volume = {48}, number = {1}, pages = {18--29}, abstract = {

In this paper, we consider a self-adaptive extrapolated Gauss-Seidel method for solving the Hermitian positive definite linear systems. Based on optimization models, self-adaptive optimal factor is given. Moreover, we prove the convergence of the self-adaptive extrapolated Gauss-Seidel method without any constraints on optimal factor. Finally, the numerical examples show that the self-adaptive extrapolated Gauss-Seidel method is effective and practical in iteration number.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v48n1.15.02}, url = {http://global-sci.org/intro/article_detail/jms/9907.html} }
TY - JOUR T1 - Self-Adaptive Extrapolated Gauss-Seidel Iterative Methods AU - Meng , Guo-Yan AU - Wen , Rui-Ping JO - Journal of Mathematical Study VL - 1 SP - 18 EP - 29 PY - 2015 DA - 2015/03 SN - 48 DO - http://doi.org/10.4208/jms.v48n1.15.02 UR - https://global-sci.org/intro/article_detail/jms/9907.html KW - Hermitian positive definite, Gauss-Seidel iteration, self-adaptive, extrapolated, linear systems. AB -

In this paper, we consider a self-adaptive extrapolated Gauss-Seidel method for solving the Hermitian positive definite linear systems. Based on optimization models, self-adaptive optimal factor is given. Moreover, we prove the convergence of the self-adaptive extrapolated Gauss-Seidel method without any constraints on optimal factor. Finally, the numerical examples show that the self-adaptive extrapolated Gauss-Seidel method is effective and practical in iteration number.

Meng , Guo-Yan and Wen , Rui-Ping. (2015). Self-Adaptive Extrapolated Gauss-Seidel Iterative Methods. Journal of Mathematical Study. 48 (1). 18-29. doi:10.4208/jms.v48n1.15.02
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