Numerische Mathematik

, Volume 48, Issue 5, pp 543-560

First online:

The rate of convergence of Conjugate Gradients

  • A. van der SluisAffiliated withMathematical Institute, University of Utrecht
  • , H. A. van der VorstAffiliated withDepartment of Mathematics, University of Technology

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It has been observed that the rate of convergence of Conjugate Gradients increases when one or more of the extreme Ritz values have sufficiently converged to the corresponding eigenvalues (the “superlinear convergence” of CG). In this paper this will be proved and made quantitative. It will be shown that a very modest degree of convergence of an extreme Ritz value already suffices for an increased rate of convergence to occur.

Subject Classifications

AMS (MOS): 65F10 CR: G.1.3