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Conference publicationsAbstractsXIX conferenceNumerical study of convergence of Krylov subspace methods on parameterized test matricesMoscow, Lenin avenue, 61/1, 28 1 pp. (accepted)Krylov subspace methods considered to most effective iterative techniques for SLAE solving assuming that no information is provided about underlying differential problem. The main idea of such methods is to look for the approximate solution of the form $$x=x_0 + y_1v_1 + y_2v_2 + ... + y_mv_m$$ where $v_1$, $v_2$, ..., $v_m$ is a basis of Krylov subspace K, $y_1$, $y_2$, ..., $y_m$ - coefficients, $x_0$ - initial approximation. Some theoretical results on the convergence of Krylov subspace methods are available in literature. Nevertheless there is a necessity of numerical testing of these methods. The main goal of this paper is to investigate the influence of matrix spectrum properties on convergence of some Krylov subspace methods (GMRES, BiCG, BiCGStab, QMR, CGS). For this purpose parameterized test matrices were built. Spectral properties of these matrices may be tuned by setting values of a few parameters. Using these matrices we compared convergence on matrices with different portraits under fixed spectrum, matrices with different degree of some eigenvalues, etc. The results of these numerical experiments are presented in this paper.
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