BiCR variants of the hybrid BiCG methods for solving linear systems with nonsymmetric matrices

  • Authors:

  • Kuniyoshi Abe;Gerard L. G. Sleijpen

  • Affiliations:

  • Faculty of Economics and Information, Gifu Shotoku University, Nakauzura, Gifu 500-8288, Japan;Department of Mathematics, Utrecht University, P.O. Box 80.010, 3508 TA Utrecht, The Netherlands

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2010

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Abstract

We propose Bi-Conjugate Residual (BiCR) variants of the hybrid Bi-Conjugate Gradient (BiCG) methods (referred to as the hybrid BiCR variants) for solving linear systems with nonsymmetric coefficient matrices. The recurrence formulas used to update an approximation and a residual vector are the same as those used in the corresponding hybrid BiCG method, but the recurrence coefficients are different; they are determined so as to compute the coefficients of the residual polynomial of BiCR. From our experience it appears that the hybrid BiCR variants often converge faster than their BiCG counterpart. Numerical experiments show that our proposed hybrid BiCR variants are more effective and less affected by rounding errors. The factor in the loss of convergence speed is analyzed to clarify the difference of the convergence between our proposed hybrid BiCR variants and the hybrid BiCG methods.