Kaczmarz-type inner-iteration preconditioned flexible GMRES methods for consistent linear systems
Kaczmarz-type inner-iteration preconditioned flexible GMRES methods for consistent linear systems
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DOI：
10.1137/20m1344937
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发表时间：
2020-06
期刊：
影响因子：
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通讯作者：
Yi-Shu Du;K. Hayami;Ning Zheng;K. Morikuni;Junfeng Yin
中科院分区：
文献类型：
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作者：
Yi-Shu Du;K. Hayami;Ning Zheng;K. Morikuni;Junfeng Yin
我们提出了用贪婪和随机的Kaczmarz内迭代作为右预条件柔性GMRES方法求解相容线性方程组的预条件，并提出了一种调整内迭代次数和松弛参数的参数调整策略。我们还给出了求解相容线性方程组的右预条件柔性GMRES的理论证明。对超定和欠定线性系统的数值实验表明，该方法在总的计算时间上优于基于NE-SOR内迭代的GMRES方法。
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.