Numerische Mathematik

, Volume 48, Issue 5, pp 499-523

First online:

On the rate of convergence of the preconditioned conjugate gradient method

  • Owe AxelssonAffiliated withDepartment of Computer Sciences, Lund University
  • , Gunhild LindskogAffiliated withDepartment of Computer Sciences, Chalmers University of Technology

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We derive new estimates for the rate of convergence of the conjugate gradient method by utilizing isolated eigenvalues of parts of the spectrum. We present a new generalized version of an incomplete factorization method and compare the derived estimates of the number of iterations with the number actually found for some elliptic difference equations and for a similar problem with a model empirical distribution function.

Subject Classifications

AMS(MOS): 65F10 CR: G1.3