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The rate of convergence of Conjugate Gradients

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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.

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Authors and Affiliations

  1. Mathematical Institute, University of Utrecht, Budapestlaan 6, Utrecht, The Netherlands

    A. van der Sluis

  2. Department of Mathematics, University of Technology, Julianalaan 132, Delft, The Netherlands

    H. A. van der Vorst

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  1. A. van der Sluis
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  2. H. A. van der Vorst
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van der Sluis, A., van der Vorst, H.A. The rate of convergence of Conjugate Gradients. Numer. Math. 48, 543–560 (1986). https://doi.org/10.1007/BF01389450

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