Improving the convergence behaviour of BiCGSTAB by applying <i>D</i>-norm minimization

• Su Lijiong

  Department of Computer Science

• Imakura Akira

  Department of Computer Science

• Tadano Hiroto

  Department of Computer Science

• Sakurai Tetsuya

  Department of Computer Science CREST

Abstract

In this article, we deal with the iterative methods for solving unsymmetric linear systems, especially BiCGSTAB. The introduced parameter in BiCGSTAB at each iteration is selected to minimize the 2-norm of the residual vector. Here, we suggest another way to select the parameter by the idea of weighting used in Weighted GMRES. By our procedure, more importance is assigned to the larger entry of the residual vector so that faster convergence can be expected. In numerical experiments, it is shown that our procedure is efficient compared with the original BiCGSTAB.

Journal

• JSIAM Letters

  JSIAM Letters 7 (0), 37-40, 2015

  The Japan Society for Industrial and Applied Mathematics

Keywords

• linear system
• Krylov subspace method
• BiCGSTAB
• \textit{D}-norm

Details

• CRID: 1390282680276706432
• NII Article ID: 130005068708
• DOI: 10.14495/jsiaml.7.37
• ISSN: 18830617
• ISSN: 18830609
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed