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An Automatic Procedure for Updating the Block Size in the Block Conjugate Gradient Method for Solving Linear Systems

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Abstract

The paper considers the problem of constructing an efficient automatic procedure for reducing the block size in the block conjugate gradient method insuring that the resulting rate of convergence is comparable with that of the block conjugate gradient method with constant block size. The numerical results provided show that, independently of the type of distribution of the smallest eigenvalues of the preconditioned matrix, the procedure suggested always leads to a decrease of the arithmetic costs with respect to those of the block method with constant block size. Bibliography: 8 titles.

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Authors and Affiliations

  1. Computing Center of the Russian Academy of Sciences, Russia

    A. A. Nikishin

  2. Scientific Research Computing Center of the, Moscow State University, Russia

    A. Yu. Yeremin

Authors
  1. A. A. Nikishin
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  2. A. Yu. Yeremin
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Nikishin, A.A., Yeremin, A.Y. An Automatic Procedure for Updating the Block Size in the Block Conjugate Gradient Method for Solving Linear Systems. Journal of Mathematical Sciences 114, 1844–1853 (2003). https://doi.org/10.1023/A:1022462721147

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  • DOI: https://doi.org/10.1023/A:1022462721147

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