A Class of Product-type Methods Based on Lanczos Process

DOI 14 Citations 27 References

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Other Title
  • ランチョス・プロセスに基づく積型反復解法

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Abstract

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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Details 詳細情報について

  • CRID
    1390282680745109504
  • NII Article ID
    110001883608
  • NII Book ID
    AN10367166
  • DOI
    10.11540/jsiamt.5.4_343
  • ISSN
    24240982
  • Text Lang
    ja
  • Data Source
    • JaLC
    • CiNii Articles
  • Abstract License Flag
    Disallowed

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