Necessary and sufficient conditions for the convergence of Orthomin(k) on singular and inconsistent linear systems |
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| Authors: | Shao-Liang Zhang Yoshio Oyanagi Masaaki Sugihara |
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| Institution: | (1) Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan; e-mail: zhang@zzz.t.u-tokyo.ac.jp, JP;(2) Department of Information Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan; e-mail: oyanagi@is.s.u-tokyo.ac.jp, JP;(3) Department of Computational Science and Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan; e-mail: sugihara@cse.nagoya-u.ac.jp, JP |
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| Abstract: | 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.
Received April 1, 1995 / Revised version received October 1, 1997 / Published online July 12, 2000 |
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| Keywords: | Mathematics Subject Classification (1991): 65F10 |
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