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The Gauss-Seidel iterative method with the preconditioning matrix (I +S +S m )

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Abstract

We propose a preconditioned iterative method with the preconditioning matrixP sm =I +S +S m forAx =b, whereA is an irreducibly diagonal dominantZ-matrix with unit diagonal. The convergence property and the comparison theorem of the proposed method are discussed. Moreover, some numerical examples are reported to confirm the theoretical analysis.

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Authors and Affiliations

  1. Department of Information Science, Faculty of Informatics, Okayama University of Science, 700-0005, Okayama, Japan

    Munenori Morimoto, Kyouji Harada, Michio Sakakihara & Hideo Sawami

Authors
  1. Munenori Morimoto
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  2. Kyouji Harada
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  3. Michio Sakakihara
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  4. Hideo Sawami
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Corresponding author

Correspondence to Michio Sakakihara.

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Morimoto, M., Harada, K., Sakakihara, M. et al. The Gauss-Seidel iterative method with the preconditioning matrix (I +S +S m ). Japan J. Indust. Appl. Math. 21, 25–34 (2004). https://doi.org/10.1007/BF03167430

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  • DOI: https://doi.org/10.1007/BF03167430

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