Inner-iteration Preconditioning with Symmetric Splitting Matrices for Symmetric Singular Linear Systems

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  • 対称な特異線形系に対する対称な分離行列を持つ内部反復前処理

Abstract

<p>Abstract. We give conditions such that the conjugate gradient (CG) method and the minimal residual (MINRES) method preconditioned by the stationary inner iterations with symmetric splitting matrices respectively determine a solution of a symmetric linear system including the singular case. These results are applied to the inner-iteration preconditioned CG and MINRES-type methods for solving least squares and minimum-norm solution problems in the rank-deficient case to complement the convergence theory of these methods in [Morikuni, Hayami, SIAM J. Matrix Appl. Anal., 34 (2013), 1–22].</p>

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Details

  • CRID
    1390845713069829760
  • NII Article ID
    130007618981
  • DOI
    10.11540/jsiamt.29.1_62
  • ISSN
    24240982
  • Text Lang
    ja
  • Data Source
    • JaLC
    • CiNii Articles
    • KAKEN
    • Crossref
  • Abstract License Flag
    Disallowed

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