Improving the convergence behaviour of BiCGSTAB by applying D-norm minimization

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 weigh...

Full description

Saved in:
Bibliographic Details
Published inJSIAM Letters Vol. 7; pp. 37 - 40
Main Authors Su, Lijiong, Imakura, Akira, Tadano, Hiroto, Sakurai, Tetsuya
Format Journal Article
LanguageEnglish
Published The Japan Society for Industrial and Applied Mathematics 2015
Subjects
BiCGSTAB
Krylov subspace method
linear system
textit{D}-norm
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1883-0609
1883-0617
DOI:10.14495/jsiaml.7.37