On the convergence rate of the conjugate gradients in presence of rounding errors

Summary We investigate here rounding error effects on the convergence rate of the conjugate gradients. More precisely, we analyse on both theoretical and experimental basis how finite precision arithmetic affects known bounds on iteration numbers when the spectrum of the system matrix presents small or large isolated eigenvalues.The present work was supported by the Programme d'impulsion en Technologie l'Information, financed by Belgian State, under contract No. IT/IF/14Supported by the Fonds National de la Recherche Scientifique, Chargé de recherches