BIT Numerical Mathematics

, Volume 29, Issue 4, pp 635–657

The effect of ordering on preconditioned conjugate gradients

  • Iain S. Duff
  • Gérard A. Meurant
Preconditioned Conjugate Gradient Methods


We investigate the effect of the ordering of the unknowns on the convergence of the preconditioned conjugate gradient method. We examine a wide range of ordering methods including nested dissection, minimum degree, and red-black and consider preconditionings without fill-in. We show empirically that there can be a significant difference in the number of iterations required by the conjugate gradient method and suggest reasons for this marked difference in performance.

We also consider the effect of orderings when an incomplete factorization which allows some fill-in is performed. We consider the effect of automatically controlling the sparsity of the incomplete factorization through drop tolerances and level of fill-in.

AMS Classification



Sparse matrices preconditioning ordering strategies conjugate gradients 


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Copyright information

© BIT Foundations 1989

Authors and Affiliations

  • Iain S. Duff
    • 1
    • 2
  • Gérard A. Meurant
    • 1
    • 2
  1. 1.Computer Science and Systems DivisionHarwell LaboratoryOxonUK
  2. 2.CEA, Centre d'Etudes de Limeil-ValentonVilleneuve St GeorgesFrance

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