特異な係数行列をもつ連立一次方程式に対するCR法の収束性  [in Japanese] Convergence Theory of the CR Method for Linear Singular Systems  [in Japanese]

Access this Article

Search this Article

Author(s)

Abstract

The convergence rate of the residual vector of the conjugate residual (CR) method is well known for a linear system Ax=b, where A is nonsingular. In this paper, we consider the convergence theory of the CR method for a linear system, where the coefficient matrix is singular. First, when we give a certain condition, we show that the algorithm of the CR method can be decomposed into components in the range space of A, which we denote by R(A), and the orthogonal complement space of R(A). Secondly, we present a bound of the residual norms of the CR method in R(A). These two results imply that we can derive an estimate of the error bound for a linear singular system. Moreover, we show necessary and sufficient conditions for the convergence of the CR method starting with an arbitrary right-hand side vector. As a byproduct, the residual norm of the CR method for symmetric positive semi-definite coefficient matrices is also analyzed.

Journal

  • Transactions of the Japan Society for Industrial and Applied Mathematics

    Transactions of the Japan Society for Industrial and Applied Mathematics 9(1), 1-13, 1999

    The Japan Society for Industrial and Applied Mathematics

References:  11

Cited by:  3

Codes

  • NII Article ID (NAID)
    110001883710
  • NII NACSIS-CAT ID (NCID)
    AN10367166
  • Text Lang
    JPN
  • Article Type
    Journal Article
  • ISSN
    09172246
  • NDL Article ID
    4679479
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z15-727
  • Data Source
    CJP  CJPref  NDL  NII-ELS  J-STAGE 
Page Top