導出過程に着目したCGS法の前処理付きアルゴリズム  [in Japanese] Preconditioned Algorithm of the CGS Method Focusing on Its Deriving Process  [in Japanese]

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Abstract

本稿ではBiCG法からCGS法を導出する過程に付随する数理的特性に着目し改善したCGS法の前処理付きアルゴリズムを提案する.また,本改善アルゴリズムの合理性について議論し,数値実験により本改善アルゴリズムの有用性を確認する.さらに,クリロフ部分空間の観点から,従来版と改善版との数理構造についても解析する.本改善は,前処理付きCGS法に限らず,初期シャドウ残差ベクトルを伴う前処理付きアルゴリズム全般に当てはまる.

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.

Journal

  • Transactions of the Japan Society for Industrial and Applied Mathematics

    Transactions of the Japan Society for Industrial and Applied Mathematics 23(2), 253-286, 2013

    The Japan Society for Industrial and Applied Mathematics

References:  18

Codes

  • NII Article ID (NAID)
    110009616463
  • NII NACSIS-CAT ID (NCID)
    AN10367166
  • Text Lang
    JPN
  • Article Type
    ART
  • ISSN
    09172246
  • NDL Article ID
    024798811
  • NDL Call No.
    Z15-727
  • Data Source
    CJP  NDL  NII-ELS  J-STAGE 
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