BiCGStab(ℓ) for Families of Shifted Linear Systems

@article{Frommer2003BiCGStabFF,
  title={BiCGStab(ℓ) for Families of Shifted Linear Systems},
  author={Andreas Frommer},
  journal={Computing},
  year={2003},
  volume={70},
  pages={87-109}
}
We consider a seed system Ax = b together with a shifted linear system of the form We develop modifications of the BiCGStab(ℓ) method which allow to solve the seed and the shifted system at the expense of just the matrix-vector multiplications needed to solve Ax = b via BiCGStab(ℓ). On the shifted system, these modifications do not perform the corresponding BiCGStab(ℓ)-method, but we show, that in the case that A is positive real and σ ≥ 0, the resulting method is still a well-smoothed variant… CONTINUE READING
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