A strategy of reducing the inner iteration counts for the variable preconditioned GCR({$\vc{m}$}) method

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概要

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• It has been clarified by numerical experiments that a variable preconditioned GCR($m$) method using the SOR method is efficient for solving a sparse linear system. However there are cases that the residual norm of variable preconditioned GCR method stagnates. Then the inner iteration counts increase, and more computation time is required. Therefore, we propose a strategy to reduce the inner iteration counts in case of stagnation of the residual norm by using a certain parameter related to convergence behavior. Numerical experiments show that our strategy is indeed effective.

著者

• Aihara Kensuke

  Graduate School of Science, Tokyo University of Science

• Ishiwata Emiko

  Department of Mathematical Information Science, Tokyo University of Science

• Abe Kuniyoshi

  Faculty of Economics and Information, Gifu Shotoku University

関連論文

• A strategy of reducing the inner iteration counts for the variable preconditioned GCR({$\vc{m}$}) method
• Discrete hungry integrable systems related to matrix eigenvalue and their local analysis by center manifold theory (Expansion of Integrable Systems)
• Improved SOR Method with Orderings and Direct Methods
• An alternative implementation of the IDRstab method saving vector updates

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