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Necessary and sufficient conditions for the convergence of Orthomin(k) on singular and inconsistent linear systems

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Summary.

We consider the convergence of Orthomin(k) on singular and inconsistent linear systems. Criteria for the breakdown of Orthomin(k) are discussed and analyzed. Moreover, necessary and sufficient conditions for the convergence of Orthomin(k) for any right hand side are given, and a rate of convergence is provided as well. Finally, numerical experiments are shown to confirm the convergence theorem.

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Authors and Affiliations

  1. Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan; e-mail: zhang@zzz.t.u-tokyo.ac.jp, , , , , , JP

    Shao-Liang Zhang

  2. Department of Information Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan; e-mail: oyanagi@is.s.u-tokyo.ac.jp, , , , , , JP

    Yoshio Oyanagi

  3. Department of Computational Science and Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan; e-mail: sugihara@cse.nagoya-u.ac.jp, , , , , , JP

    Masaaki Sugihara

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  1. Shao-Liang Zhang
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  2. Yoshio Oyanagi
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  3. Masaaki Sugihara
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Received April 1, 1995 / Revised version received October 1, 1997 / Published online July 12, 2000

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Zhang, SL., Oyanagi, Y. & Sugihara, M. Necessary and sufficient conditions for the convergence of Orthomin(k) on singular and inconsistent linear systems. Numer. Math. 87, 391–405 (2000). https://doi.org/10.1007/s002110000185

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  • DOI: https://doi.org/10.1007/s002110000185

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