Preconditioned Algorithm of the CGS Method Focusing on Its Deriving Process

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  • Itoh Shoji
    Information Technology Center, The University of Tokyo
  • Sugihara Masaaki
    Graduate School of Information Science and Technology, The University of Tokyo

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  • 導出過程に着目したCGS法の前処理付きアルゴリズム
  • ドウシュツ カテイ ニ チャクモク シタ CGSホウ ノ マエショリ ツキ アルゴリズム

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In this paper, improved preconditioned algorithms of the CGS method (improved PCGS) are proposed. These improved PCGS algorithms retain some mathematical properties that are accompanied with the CGS derivation from the BiCG method. Rationalities of these improved algorithms are discussed and numerical results illustrate the availability of them. Further, mathematical structure between the conventional PCGS and the improved PCGS is analyzed from the viewpoint of the Krylov subspace. This improvement can be applied to preconditioned algorithms involving the initial shadow residual vector, not only to the PCGS.

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