ランチョス・プロセスに基づく積型反復解法

書誌事項

タイトル別名
  • A Class of Product-type Methods Based on Lanczos Process

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説明

In this paper, we propose a unification of results involving product-type methods for the iterative solution of nonsymmetric linear systems. A characteristic of this class of methods(that includes CGS. Bi-CGSTAB, and Bi-CGSTAB2)is the relationship γ_n=H_n(A)R_n(A)γ_0 where γ_n is the residual vector corresponding to the n-th iterate x_n, and R_n is the Lanczos polynomial generated from Bi-CG. The poly-nomial H_n in the product H_n(A)R_n(A) is chosen to speed up and/or stabilize convergence, while satisfying a standard three-term recurrence relations. Such product-type methods can be regarded as generalizations of Bi-CGSTAB. From the unification, we can see how CGS, Bi-CGSTAB, and Bi-CGSTAB2 fit into a more general framework.

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被引用文献 (14)*注記

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参考文献 (27)*注記

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詳細情報 詳細情報について

  • CRID
    1390282680745109504
  • NII論文ID
    110001883608
  • NII書誌ID
    AN10367166
  • DOI
    10.11540/jsiamt.5.4_343
  • ISSN
    24240982
  • 本文言語コード
    ja
  • データソース種別
    • JaLC
    • CiNii Articles
  • 抄録ライセンスフラグ
    使用不可

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