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The effect of the spectral properties of the linear system matrix on the convergence of some krylov methods

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The article presents the results of numerical analysis of the effect of various characteristics of the matrix of a system of linear algebraic equations on the convergence of some Krylov methods (BiCG, BiCGStab, QMR, GMRES, and CGS). The study uses test linear equation systems with matrices generated by specially developed algorithms. The test matrices are unsymmetric sparse and their spectral characteristics are controlled by appropriate specification of several parameters.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

    I. M. Nikol’skii

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  1. I. M. Nikol’skii
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Correspondence to I. M. Nikol’skii.

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Translated from Prikladnaya Matematika i Informatika, No. 38, pp. 66–76, 2011.

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Nikol’skii, I.M. The effect of the spectral properties of the linear system matrix on the convergence of some krylov methods. Comput Math Model 23, 319–328 (2012). https://doi.org/10.1007/s10598-012-9140-3

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  • DOI: https://doi.org/10.1007/s10598-012-9140-3

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