Analysis of the structure of the Krylov subspace in various preconditioned CGS algorithms

@article{Itoh2016AnalysisOT,
  title={Analysis of the structure of the Krylov subspace in various preconditioned CGS algorithms},
  author={Shoji Itoh and Masaaki Sugihara},
  journal={ArXiv},
  year={2016},
  volume={abs/1603.00176}
}
An improved preconditioned CGS (PCGS) algorithm has recently been proposed, and it performs much better than the conventional PCGS algorithm. In this paper, the improved PCGS algorithm is verified as a coordinative to the left-preconditioned system; this is done by comparing, analyzing, and executing numerical examinations of various PCGS algorithms, including the most recently proposed one. We show that the direction of the preconditioned system for the CGS method is determined by the… Expand
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A theorem that defines the direction of a preconditioned system for the bi-conjugate gradient (BiCG) method is presented, and it is shown that the direction is switched by construction and by the settings of the initial shadow residual vector. Expand

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