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arXiv · 2006.10818

Kaczmarz-type inner-iteration preconditioned flexible GMRES methods for consistent linear systems

Yi-Shu Du·Ken Hayami·Ning Zheng·Keiichi Morikuni·Jun-Feng Yin
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Abstract

We propose using greedy and randomized Kaczmarz inner-iterations as preconditioners for the right-preconditioned flexible GMRES method to solve consistent linear systems, with a parameter tuning strategy for adjusting the number of inner iterations and the relaxation parameter. We also present theoretical justifications of the right-preconditioned flexible GMRES for solving consistent linear systems. Numerical experiments on overdetermined and underdetermined linear systems show that the proposed method is superior to the GMRES method preconditioned by NE-SOR inner iterations in terms of total CPU time.

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Yi-Shu Du, Ken Hayami, Ning Zheng, Keiichi Morikuni, Jun-Feng Yin. 2020-06-18. Kaczmarz-type inner-iteration preconditioned flexible GMRES methods for consistent linear systems. https://arxiv.org/abs/2006.10818

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