Communications on Applied Mathematics and Computation ›› 2019, Vol. 1 ›› Issue (3): 435-447.doi: 10.1007/s42967-019-00022-z

• ORIGINAL PAPER • 上一篇    下一篇

A Note on the Adaptive Simpler Block GMRES Method

Qiaohua Liu1, Lei Yao1, Aijing Liu2   

  1. 1 Department of Mathematics, Shanghai University, Shanghai 200444, China;
    2 School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong Province, China
  • 收稿日期:2018-07-10 修回日期:2018-08-21 出版日期:2019-09-20 发布日期:2019-09-09
  • 通讯作者: Qiaohua Liu, Lei Yao, Aijing Liu E-mail:qhliu@shu.edu.cn;yaolei01@shu.edu.cn;ajliu79@163.com
  • 基金资助:
    This work was supported by the National Natural Science Foundation of China (11701320), and the Shandong Provincial Natural Science Foundation of China (ZR2016AM04).

A Note on the Adaptive Simpler Block GMRES Method

Qiaohua Liu1, Lei Yao1, Aijing Liu2   

  1. 1 Department of Mathematics, Shanghai University, Shanghai 200444, China;
    2 School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong Province, China
  • Received:2018-07-10 Revised:2018-08-21 Online:2019-09-20 Published:2019-09-09
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (11701320), and the Shandong Provincial Natural Science Foundation of China (ZR2016AM04).

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摘要： The adaptive simpler block GMRES method was investigated by Zhong et al. (J Comput Appl Math 282:139-156, 2015) where the condition number of the adaptively chosen basis for the Krylov subspace was evaluated. In this paper, the new upper bound for the condition number is investigated. Numerical tests show that the new upper bound is tighter.

关键词: Large-scale nonsymmetric linear system, Krylov subspace method, Adaptive simpler block GMRES, Condition number

Abstract: The adaptive simpler block GMRES method was investigated by Zhong et al. (J Comput Appl Math 282:139-156, 2015) where the condition number of the adaptively chosen basis for the Krylov subspace was evaluated. In this paper, the new upper bound for the condition number is investigated. Numerical tests show that the new upper bound is tighter.

Key words: Large-scale nonsymmetric linear system, Krylov subspace method, Adaptive simpler block GMRES, Condition number

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