Stability of GPBiCG_AR Method Based on Minimization of Associate Residual

  • Moe Thuthu
  • Seiji Fujino
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5081)


GPBi-CG method is an attractive iterative method for the solution of a linear system of equations with nonsymmetric coefficient matrix. However, the popularity of GPBi-CG method has diminished over time except for the minority. In this paper, we consider a new algorithm based on minimization of the associate residual of 2-norm in place of reconstruction of the algorithm. We refer to a method with new algorithm as GPBiCG with Associate Residual (abbreviated as GPBiCG_AR) method. Moreover we will introduce preconditioned GPBiCG_AR (abbreviated as P_GPBiCG_AR). Then, we will support that GPBiCG_AR and P_GPBiCG_AR methods yield safety convergence through numerical experiments.


GPBi-CG GPBiCG_AR nonsymmetric coefficient matrix Associate Residual precondition 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Moe Thuthu
    • 1
  • Seiji Fujino
    • 2
  1. 1.Graduate School of Information Science and Electrical Engineering 
  2. 2.Research Institute for Information TechnologyKyushu UniversityJapan

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